{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":45281,"title":"A \"Complex\" Converter: Rectangular Form \u003c-\u003e Polar Form","description":"*BACKGROUND / MOTIVATION:*\r\n\r\nComplex numbers can be an important tool in an electrical engineer's toolbox because they can help us describe / work with sinusoidal signals.\r\n\r\nSinusoidal signals can be found all over the place in day-to-day life (in music, light, communication systems, power systems, etc.):\r\n\r\n* \"Why Study Sinusoids?\": \u003chttps://www.youtube.com/watch?v=yXjXJ5OlNyQ\u003e\r\n* \"Euler's formula\": \u003chttps://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\u003e\r\n\r\nWhen working with complex numbers, sometimes it's easier to work with the \"rectangular/Cartesian form\" (z = x + j*y) and sometimes it's easier to work with the \"polar form\" (r ∠ θ).\r\n\r\n_An analogy:_\r\n\r\n* Using the rectangular form is sometimes like using decimals: it can make the numbers easier to add / subtract\r\n* Using the polar form is sometimes like using fractions: it can the numbers easier to multiply / divide\r\n* In the end, the two forms are equivalent, but sometimes they're easier to work with in one form instead of another.\r\n\r\n*PROBLEM DESCRIPTION*\r\n\r\nWrite a function which converts between the rectangular form and the polar form.\r\n\r\nYou can view a comparison of the two forms here:\r\n\u003chttps://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-complex-numbers\u003e\r\n\r\nThe variable \"form\" will be used to determine whether the function converts from rectangular to polar or from polar to rectangular.\r\n\r\nThe function takes the following inputs:\r\n\r\n* \"input1\" - a variable which is either \"x\" (the real component in rectangular form) or \"r\" (the radius in polar form)\r\n* \"input2\" - a variable which is either \"y\" (the complex component in rectangular form) or \"theta\" (the angle, in degrees, in polar form)\r\n* \"form\" - a variable which is set to either \"r2p\" (to convert from rectangular to polar) or \"p2r\" (to convert from polar to rectangular)\r\n\r\nThe function will output the variable \"output\" in the form of a column vector [output1;output2] where:\r\n\r\n* \"output1\" - a component of the output which is either \"x\" (the real component in rectangular form) or \"r\" (the radius in polar form)\r\n* \"output2\" - a component of the output which is either \"y\" (the complex component in rectangular form) or \"theta\" (the positive angle, in degrees, in polar form)\r\n\r\nThe test suite will round the components of your output vector to 4 decimal places.\r\n\r\n*FEEDBACK*\r\n\r\nPlease feel free to leave feedback on this problem in the comments!  :)","description_html":"\u003cp\u003e\u003cb\u003eBACKGROUND / MOTIVATION:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eComplex numbers can be an important tool in an electrical engineer's toolbox because they can help us describe / work with sinusoidal signals.\u003c/p\u003e\u003cp\u003eSinusoidal signals can be found all over the place in day-to-day life (in music, light, communication systems, power systems, etc.):\u003c/p\u003e\u003cul\u003e\u003cli\u003e\"Why Study Sinusoids?\": \u003ca href = \"https://www.youtube.com/watch?v=yXjXJ5OlNyQ\"\u003ehttps://www.youtube.com/watch?v=yXjXJ5OlNyQ\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\"Euler's formula\": \u003ca href = \"https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\"\u003ehttps://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eWhen working with complex numbers, sometimes it's easier to work with the \"rectangular/Cartesian form\" (z = x + j*y) and sometimes it's easier to work with the \"polar form\" (r ∠ θ).\u003c/p\u003e\u003cp\u003e\u003ci\u003eAn analogy:\u003c/i\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eUsing the rectangular form is sometimes like using decimals: it can make the numbers easier to add / subtract\u003c/li\u003e\u003cli\u003eUsing the polar form is sometimes like using fractions: it can the numbers easier to multiply / divide\u003c/li\u003e\u003cli\u003eIn the end, the two forms are equivalent, but sometimes they're easier to work with in one form instead of another.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003ePROBLEM DESCRIPTION\u003c/b\u003e\u003c/p\u003e\u003cp\u003eWrite a function which converts between the rectangular form and the polar form.\u003c/p\u003e\u003cp\u003eYou can view a comparison of the two forms here: \u003ca href = \"https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-complex-numbers\"\u003ehttps://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-complex-numbers\u003c/a\u003e\u003c/p\u003e\u003cp\u003eThe variable \"form\" will be used to determine whether the function converts from rectangular to polar or from polar to rectangular.\u003c/p\u003e\u003cp\u003eThe function takes the following inputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\"input1\" - a variable which is either \"x\" (the real component in rectangular form) or \"r\" (the radius in polar form)\u003c/li\u003e\u003cli\u003e\"input2\" - a variable which is either \"y\" (the complex component in rectangular form) or \"theta\" (the angle, in degrees, in polar form)\u003c/li\u003e\u003cli\u003e\"form\" - a variable which is set to either \"r2p\" (to convert from rectangular to polar) or \"p2r\" (to convert from polar to rectangular)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe function will output the variable \"output\" in the form of a column vector [output1;output2] where:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\"output1\" - a component of the output which is either \"x\" (the real component in rectangular form) or \"r\" (the radius in polar form)\u003c/li\u003e\u003cli\u003e\"output2\" - a component of the output which is either \"y\" (the complex component in rectangular form) or \"theta\" (the positive angle, in degrees, in polar form)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe test suite will round the components of your output vector to 4 decimal places.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFEEDBACK\u003c/b\u003e\u003c/p\u003e\u003cp\u003ePlease feel free to leave feedback on this problem in the comments!  :)\u003c/p\u003e","function_template":"function [output] = complexConverter(input1, input2, form)\r\n  % write a function which converts from rectangular to polar and polar to rectangular\r\nend","test_suite":"%%Test1\r\ninput1 = 2; %x\r\ninput2 = 2; %y\r\nform = 'r2p';\r\noutput1 = 2.8284;\r\noutput2 = 45;\r\noutput = [output1;output2];\r\nassert(isequal(round(complexConverter(input1, input2, form),4),output))\r\n%%Test2\r\ninput1 = 3; %radius\r\ninput2 = 60; %degrees\r\nform = 'p2r';\r\noutput1 = 1.5000;\r\noutput2 = 2.5981;\r\noutput = [output1;output2];\r\nassert(isequal(round(complexConverter(input1, input2, form),4),output))\r\n%%Test3\r\ninput1 = 3; %x\r\ninput2 = -4; %y\r\nform = 'r2p';\r\noutput1 = 5.0000;\r\noutput2 = 306.8699;\r\noutput = [output1;output2];\r\nassert(isequal(round(complexConverter(input1, input2, form),4),output))\r\n%%Test4\r\ninput1 = 7; %radius\r\ninput2 = 225; %degrees\r\nform = 'p2r';\r\noutput1 = -4.9497;\r\noutput2 = -4.9497;\r\noutput = [output1;output2];\r\nassert(isequal(round(complexConverter(input1, input2, form),4),output))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":377536,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-28T03:12:54.000Z","updated_at":"2025-12-29T14:25:32.000Z","published_at":"2020-02-25T00:35:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBACKGROUND / MOTIVATION:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplex numbers can be an important tool in an electrical engineer's toolbox because they can help us describe / work with sinusoidal signals.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSinusoidal signals can be found all over the place in day-to-day life (in music, light, communication systems, power systems, etc.):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"Why Study Sinusoids?\\\":\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=yXjXJ5OlNyQ\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.youtube.com/watch?v=yXjXJ5OlNyQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"Euler's formula\\\":\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen working with complex numbers, sometimes it's easier to work with the \\\"rectangular/Cartesian form\\\" (z = x + j*y) and sometimes it's easier to work with the \\\"polar form\\\" (r ∠ θ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAn analogy:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing the rectangular form is sometimes like using decimals: it can make the numbers easier to add / subtract\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing the polar form is sometimes like using fractions: it can the numbers easier to multiply / divide\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the end, the two forms are equivalent, but sometimes they're easier to work with in one form instead of another.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePROBLEM DESCRIPTION\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function which converts between the rectangular form and the polar form.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can view a comparison of the two forms 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function takes the following inputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"input1\\\" - a variable which is either \\\"x\\\" (the real component in rectangular form) or \\\"r\\\" (the radius in polar form)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"input2\\\" - a variable which is either \\\"y\\\" (the complex component in rectangular form) or \\\"theta\\\" (the angle, in degrees, in polar form)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"form\\\" - a variable which is set to either \\\"r2p\\\" (to convert from rectangular to polar) or \\\"p2r\\\" (to convert from polar to rectangular)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function will output the variable \\\"output\\\" in the form of a column vector [output1;output2] where:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"output1\\\" - a component of the output which is either \\\"x\\\" (the real component in rectangular form) or \\\"r\\\" (the radius in polar form)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"output2\\\" - a component of the output which is either \\\"y\\\" (the complex component in rectangular form) or \\\"theta\\\" (the positive angle, in degrees, in polar form)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test suite will round the components of your output vector to 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFEEDBACK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease feel free to leave feedback on this problem in the comments! :)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":51137,"title":"Compute an integral of a product of sinusoids","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.8px 7.91667px; transform-origin: 150.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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alt=\"I = integral(sin(x)^m cos(x)^n, {x,0,pi})\" style=\"width: 139px; height: 44px;\" width=\"139\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5917px 7.91667px; transform-origin: 96.5917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are integers. You may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1917px 7.91667px; transform-origin: 99.1917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e but other functions are allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intSinmCosn(m,n)\r\n  y = f(m,n);\r\nend","test_suite":"%%\r\nm = 1;\r\nn = 0;\r\ny_correct = 2;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 1;\r\ny_correct = 0;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 2;\r\ny_correct = pi/2;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 2;\r\ny_correct = 2/3;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 2;\r\ny_correct = pi/8;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 2;\r\ny_correct = 4/15;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 4;\r\ny_correct = 3*pi/8;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 4;\r\ny_correct = 2/5;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 4;\r\ny_correct = pi/16;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 4;\r\ny_correct = 4/35;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 4;\r\ny_correct = 3*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 4;\r\ny_correct = 16/315;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 4;\r\ny_correct = 3*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 4;\r\ny_correct = 32/1155;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 6;\r\ny_correct = 5*pi/16;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 6;\r\ny_correct = 2/7;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 6;\r\ny_correct = 5*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 6;\r\ny_correct = 4/63;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 6;\r\ny_correct = 3*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 6;\r\ny_correct = 16/693;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 6;\r\ny_correct = 5*pi/1024;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 6;\r\ny_correct = 32/3003;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 8;\r\ny_correct = 35*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 8;\r\ny_correct = 2/9;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 8;\r\ny_correct = 7*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 8;\r\ny_correct = 4/99;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 8;\r\ny_correct = 7*pi/1024;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 8;\r\ny_correct = 16/1287;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 8;\r\ny_correct = 5*pi/2048;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 8;\r\ny_correct = 32/6435;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2*randi(9);\r\nn = m+1;\r\ny_correct = 0;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 22;\r\ny_correct = 2/23;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 28;\r\ny_correct = 2/29;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('intSinmCosn.m');\r\nillegalfns = ~isempty(strfind(filetext, 'integral')) || ~isempty(strfind(filetext, 'quad')); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-23T00:29:43.000Z","updated_at":"2026-02-22T14:27:23.000Z","published_at":"2021-03-23T00:33:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral(sin(x)^m cos(x)^n, {x,0,pi})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^\\\\pi \\\\sin^mx\\\\cos^nxdx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are integers. You may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e but other functions are allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44948,"title":"Calculate a Damped Sinusoid","description":"The equation of a damped sinusoid can be written as\r\ny = A.ⅇ^(-λt)*cos(2πft)\r\nwhere A, λ, and f are scalars and t is a vector.\r\nCalculate the output sinusoid y given the inputs below:\r\nlambda - λ\r\nT - maximum value of t\r\nN - number of elements in t\r\nAssume A = 1 and f = 1 . The vector t should be linearly spaced from 0 to T, with N elements.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 227.15px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 113.575px; transform-origin: 406.5px 113.575px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.733px 7.81667px; transform-origin: 169.733px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe equation of a damped sinusoid can be written as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.775px; text-align: left; transform-origin: 383.5px 10.775px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.0917px 7.81667px; transform-origin: 90.0917px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 90.0917px 8.375px; transform-origin: 90.0917px 8.375px; \"\u003ey = A.ⅇ^(-λt)*cos(2πft)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.775px; text-align: left; transform-origin: 383.5px 10.775px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.9833px 7.81667px; transform-origin: 18.9833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eλ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.1917px 7.81667px; transform-origin: 16.1917px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003ef\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.925px 7.81667px; transform-origin: 51.925px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are scalars and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.85px 7.81667px; transform-origin: 36.85px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a vector.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.775px; text-align: left; transform-origin: 383.5px 10.775px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93.8px 7.81667px; transform-origin: 93.8px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the output sinusoid\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.375px 7.81667px; transform-origin: 75.375px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the inputs below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 62.95px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.5px 31.475px; transform-origin: 390.5px 31.475px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.9833px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.5px 10.4917px; text-align: left; transform-origin: 362.5px 10.4917px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 27.9167px 7.81667px; transform-origin: 27.9167px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elambda -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eλ\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.9833px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.5px 10.4917px; text-align: left; transform-origin: 362.5px 10.4917px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 64.7667px 7.81667px; transform-origin: 64.7667px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - maximum value of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.9833px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.5px 10.4917px; text-align: left; transform-origin: 362.5px 10.4917px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 78.1667px 7.81667px; transform-origin: 78.1667px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - number of elements in\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.775px; text-align: left; transform-origin: 383.5px 10.775px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.8px 7.81667px; transform-origin: 26.8px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAssume\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.5417px 7.81667px; transform-origin: 19.5417px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 19.5417px 8.375px; transform-origin: 19.5417px 8.375px; \"\u003eA = 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.9583px 7.81667px; transform-origin: 13.9583px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.5417px 7.81667px; transform-origin: 19.5417px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 19.5417px 8.375px; transform-origin: 19.5417px 8.375px; \"\u003ef = 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.6417px 7.81667px; transform-origin: 39.6417px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e . The vector\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.017px 7.81667px; transform-origin: 115.017px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should be linearly spaced from 0 to\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.3083px 7.81667px; transform-origin: 17.3083px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.0583px 7.81667px; transform-origin: 34.0583px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e elements.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = damped_cos(lambda, T, N)\r\n  y = lambda + T + N;\r\nend","test_suite":"%%\r\nfiletext = fileread('damped_cos.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n%%\r\ny_correct = [1.0000 0.7246 0.1554 -0.4232 -0.7524 -0.7118 -0.3583 0.1177 0.4912 0.6065];\r\ny_test = damped_cos(0.5, 1, 10);\r\nassert( all ( abs(y_correct(:) - y_test(:)) \u003c 1e-4 ) )\r\n%% \r\ny_correct = [1.0000 -3.4903 12.1825];\r\ny_test = damped_cos(-0.5, 5, 3)\r\nassert( all ( abs(y_correct(:) - y_test(:)) \u003c 1e-4 ) )","published":true,"deleted":false,"likes_count":64,"comments_count":8,"created_by":162851,"edited_by":223089,"edited_at":"2024-09-14T15:42:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11290,"test_suite_updated_at":"2024-09-14T15:42:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-08-19T15:55:21.000Z","updated_at":"2026-04-11T17:44:21.000Z","published_at":"2019-08-29T18:09:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe equation of a damped sinusoid can be written as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = A.ⅇ^(-λt)*cos(2πft)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eλ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are scalars and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the output sinusoid\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e given the inputs below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elambda -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eλ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - maximum value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - number of elements in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . The vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should be linearly spaced from 0 to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, with\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e elements.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":45281,"title":"A \"Complex\" Converter: Rectangular Form \u003c-\u003e Polar Form","description":"*BACKGROUND / MOTIVATION:*\r\n\r\nComplex numbers can be an important tool in an electrical engineer's toolbox because they can help us describe / work with sinusoidal signals.\r\n\r\nSinusoidal signals can be found all over the place in day-to-day life (in music, light, communication systems, power systems, etc.):\r\n\r\n* \"Why Study Sinusoids?\": \u003chttps://www.youtube.com/watch?v=yXjXJ5OlNyQ\u003e\r\n* \"Euler's formula\": \u003chttps://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\u003e\r\n\r\nWhen working with complex numbers, sometimes it's easier to work with the \"rectangular/Cartesian form\" (z = x + j*y) and sometimes it's easier to work with the \"polar form\" (r ∠ θ).\r\n\r\n_An analogy:_\r\n\r\n* Using the rectangular form is sometimes like using decimals: it can make the numbers easier to add / subtract\r\n* Using the polar form is sometimes like using fractions: it can the numbers easier to multiply / divide\r\n* In the end, the two forms are equivalent, but sometimes they're easier to work with in one form instead of another.\r\n\r\n*PROBLEM DESCRIPTION*\r\n\r\nWrite a function which converts between the rectangular form and the polar form.\r\n\r\nYou can view a comparison of the two forms here:\r\n\u003chttps://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-complex-numbers\u003e\r\n\r\nThe variable \"form\" will be used to determine whether the function converts from rectangular to polar or from polar to rectangular.\r\n\r\nThe function takes the following inputs:\r\n\r\n* \"input1\" - a variable which is either \"x\" (the real component in rectangular form) or \"r\" (the radius in polar form)\r\n* \"input2\" - a variable which is either \"y\" (the complex component in rectangular form) or \"theta\" (the angle, in degrees, in polar form)\r\n* \"form\" - a variable which is set to either \"r2p\" (to convert from rectangular to polar) or \"p2r\" (to convert from polar to rectangular)\r\n\r\nThe function will output the variable \"output\" in the form of a column vector [output1;output2] where:\r\n\r\n* \"output1\" - a component of the output which is either \"x\" (the real component in rectangular form) or \"r\" (the radius in polar form)\r\n* \"output2\" - a component of the output which is either \"y\" (the complex component in rectangular form) or \"theta\" (the positive angle, in degrees, in polar form)\r\n\r\nThe test suite will round the components of your output vector to 4 decimal places.\r\n\r\n*FEEDBACK*\r\n\r\nPlease feel free to leave feedback on this problem in the comments!  :)","description_html":"\u003cp\u003e\u003cb\u003eBACKGROUND / MOTIVATION:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eComplex numbers can be an important tool in an electrical engineer's toolbox because they can help us describe / work with sinusoidal signals.\u003c/p\u003e\u003cp\u003eSinusoidal signals can be found all over the place in day-to-day life (in music, light, communication systems, power systems, etc.):\u003c/p\u003e\u003cul\u003e\u003cli\u003e\"Why Study Sinusoids?\": \u003ca href = \"https://www.youtube.com/watch?v=yXjXJ5OlNyQ\"\u003ehttps://www.youtube.com/watch?v=yXjXJ5OlNyQ\u003c/a\u003e\u003c/li\u003e\u003cli\u003e\"Euler's formula\": \u003ca href = \"https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\"\u003ehttps://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eWhen working with complex numbers, sometimes it's easier to work with the \"rectangular/Cartesian form\" (z = x + j*y) and sometimes it's easier to work with the \"polar form\" (r ∠ θ).\u003c/p\u003e\u003cp\u003e\u003ci\u003eAn analogy:\u003c/i\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eUsing the rectangular form is sometimes like using decimals: it can make the numbers easier to add / subtract\u003c/li\u003e\u003cli\u003eUsing the polar form is sometimes like using fractions: it can the numbers easier to multiply / divide\u003c/li\u003e\u003cli\u003eIn the end, the two forms are equivalent, but sometimes they're easier to work with in one form instead of another.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003ePROBLEM DESCRIPTION\u003c/b\u003e\u003c/p\u003e\u003cp\u003eWrite a function which converts between the rectangular form and the polar form.\u003c/p\u003e\u003cp\u003eYou can view a comparison of the two forms here: \u003ca href = \"https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-complex-numbers\"\u003ehttps://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-complex-numbers\u003c/a\u003e\u003c/p\u003e\u003cp\u003eThe variable \"form\" will be used to determine whether the function converts from rectangular to polar or from polar to rectangular.\u003c/p\u003e\u003cp\u003eThe function takes the following inputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\"input1\" - a variable which is either \"x\" (the real component in rectangular form) or \"r\" (the radius in polar form)\u003c/li\u003e\u003cli\u003e\"input2\" - a variable which is either \"y\" (the complex component in rectangular form) or \"theta\" (the angle, in degrees, in polar form)\u003c/li\u003e\u003cli\u003e\"form\" - a variable which is set to either \"r2p\" (to convert from rectangular to polar) or \"p2r\" (to convert from polar to rectangular)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe function will output the variable \"output\" in the form of a column vector [output1;output2] where:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\"output1\" - a component of the output which is either \"x\" (the real component in rectangular form) or \"r\" (the radius in polar form)\u003c/li\u003e\u003cli\u003e\"output2\" - a component of the output which is either \"y\" (the complex component in rectangular form) or \"theta\" (the positive angle, in degrees, in polar form)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe test suite will round the components of your output vector to 4 decimal places.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFEEDBACK\u003c/b\u003e\u003c/p\u003e\u003cp\u003ePlease feel free to leave feedback on this problem in the comments!  :)\u003c/p\u003e","function_template":"function [output] = complexConverter(input1, input2, form)\r\n  % write a function which converts from rectangular to polar and polar to rectangular\r\nend","test_suite":"%%Test1\r\ninput1 = 2; %x\r\ninput2 = 2; %y\r\nform = 'r2p';\r\noutput1 = 2.8284;\r\noutput2 = 45;\r\noutput = [output1;output2];\r\nassert(isequal(round(complexConverter(input1, input2, form),4),output))\r\n%%Test2\r\ninput1 = 3; %radius\r\ninput2 = 60; %degrees\r\nform = 'p2r';\r\noutput1 = 1.5000;\r\noutput2 = 2.5981;\r\noutput = [output1;output2];\r\nassert(isequal(round(complexConverter(input1, input2, form),4),output))\r\n%%Test3\r\ninput1 = 3; %x\r\ninput2 = -4; %y\r\nform = 'r2p';\r\noutput1 = 5.0000;\r\noutput2 = 306.8699;\r\noutput = [output1;output2];\r\nassert(isequal(round(complexConverter(input1, input2, form),4),output))\r\n%%Test4\r\ninput1 = 7; %radius\r\ninput2 = 225; %degrees\r\nform = 'p2r';\r\noutput1 = -4.9497;\r\noutput2 = -4.9497;\r\noutput = [output1;output2];\r\nassert(isequal(round(complexConverter(input1, input2, form),4),output))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":377536,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-28T03:12:54.000Z","updated_at":"2025-12-29T14:25:32.000Z","published_at":"2020-02-25T00:35:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBACKGROUND / MOTIVATION:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplex numbers can be an important tool in an electrical engineer's toolbox because they can help us describe / work with sinusoidal signals.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSinusoidal signals can be found all over the place in day-to-day life (in music, light, communication systems, power systems, etc.):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"Why Study Sinusoids?\\\":\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=yXjXJ5OlNyQ\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.youtube.com/watch?v=yXjXJ5OlNyQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"Euler's formula\\\":\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-eulers-formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen working with complex numbers, sometimes it's easier to work with the \\\"rectangular/Cartesian form\\\" (z = x + j*y) and sometimes it's easier to work with the \\\"polar form\\\" (r ∠ θ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAn analogy:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing the rectangular form is sometimes like using decimals: it can make the numbers easier to add / subtract\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing the polar form is sometimes like using fractions: it can the numbers easier to multiply / divide\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the end, the two forms are equivalent, but sometimes they're easier to work with in one form instead of another.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePROBLEM DESCRIPTION\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function which converts between the rectangular form and the polar form.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can view a comparison of the two forms here:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-complex-numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-complex-numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe variable \\\"form\\\" will be used to determine whether the function converts from rectangular to polar or from polar to rectangular.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function takes the following inputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"input1\\\" - a variable which is either \\\"x\\\" (the real component in rectangular form) or \\\"r\\\" (the radius in polar form)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"input2\\\" - a variable which is either \\\"y\\\" (the complex component in rectangular form) or \\\"theta\\\" (the angle, in degrees, in polar form)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"form\\\" - a variable which is set to either \\\"r2p\\\" (to convert from rectangular to polar) or \\\"p2r\\\" (to convert from polar to rectangular)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function will output the variable \\\"output\\\" in the form of a column vector [output1;output2] where:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"output1\\\" - a component of the output which is either \\\"x\\\" (the real component in rectangular form) or \\\"r\\\" (the radius in polar form)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"output2\\\" - a component of the output which is either \\\"y\\\" (the complex component in rectangular form) or \\\"theta\\\" (the positive angle, in degrees, in polar form)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test suite will round the components of your output vector to 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFEEDBACK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease feel free to leave feedback on this problem in the comments! :)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.8px 7.91667px; transform-origin: 150.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"I = integral(sin(x)^m cos(x)^n, {x,0,pi})\" style=\"width: 139px; height: 44px;\" width=\"139\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5917px 7.91667px; transform-origin: 96.5917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are integers. You may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1917px 7.91667px; transform-origin: 99.1917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e but other functions are allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intSinmCosn(m,n)\r\n  y = f(m,n);\r\nend","test_suite":"%%\r\nm = 1;\r\nn = 0;\r\ny_correct = 2;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 1;\r\ny_correct = 0;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 2;\r\ny_correct = pi/2;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 2;\r\ny_correct = 2/3;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 2;\r\ny_correct = pi/8;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 2;\r\ny_correct = 4/15;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 4;\r\ny_correct = 3*pi/8;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 4;\r\ny_correct = 2/5;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 4;\r\ny_correct = pi/16;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 4;\r\ny_correct = 4/35;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 4;\r\ny_correct = 3*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 4;\r\ny_correct = 16/315;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 4;\r\ny_correct = 3*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 4;\r\ny_correct = 32/1155;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 6;\r\ny_correct = 5*pi/16;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 6;\r\ny_correct = 2/7;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 6;\r\ny_correct = 5*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 6;\r\ny_correct = 4/63;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 6;\r\ny_correct = 3*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 6;\r\ny_correct = 16/693;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 6;\r\ny_correct = 5*pi/1024;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 6;\r\ny_correct = 32/3003;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 8;\r\ny_correct = 35*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 8;\r\ny_correct = 2/9;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 8;\r\ny_correct = 7*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 8;\r\ny_correct = 4/99;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 8;\r\ny_correct = 7*pi/1024;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 8;\r\ny_correct = 16/1287;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 8;\r\ny_correct = 5*pi/2048;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 8;\r\ny_correct = 32/6435;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2*randi(9);\r\nn = m+1;\r\ny_correct = 0;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 22;\r\ny_correct = 2/23;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 28;\r\ny_correct = 2/29;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('intSinmCosn.m');\r\nillegalfns = ~isempty(strfind(filetext, 'integral')) || ~isempty(strfind(filetext, 'quad')); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-23T00:29:43.000Z","updated_at":"2026-02-22T14:27:23.000Z","published_at":"2021-03-23T00:33:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral(sin(x)^m cos(x)^n, {x,0,pi})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^\\\\pi \\\\sin^mx\\\\cos^nxdx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are integers. You may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e but other functions are allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44948,"title":"Calculate a Damped Sinusoid","description":"The equation of a damped sinusoid can be written as\r\ny = A.ⅇ^(-λt)*cos(2πft)\r\nwhere A, λ, and f are scalars and t is a vector.\r\nCalculate the output sinusoid y given the inputs below:\r\nlambda - λ\r\nT - maximum value of t\r\nN - number of elements in t\r\nAssume A = 1 and f = 1 . The vector t should be linearly spaced from 0 to T, with N elements.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 227.15px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 113.575px; transform-origin: 406.5px 113.575px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.733px 7.81667px; transform-origin: 169.733px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe equation of a damped sinusoid can be written as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.775px; text-align: left; transform-origin: 383.5px 10.775px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.0917px 7.81667px; transform-origin: 90.0917px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 90.0917px 8.375px; transform-origin: 90.0917px 8.375px; \"\u003ey = A.ⅇ^(-λt)*cos(2πft)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.775px; text-align: left; transform-origin: 383.5px 10.775px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.9833px 7.81667px; transform-origin: 18.9833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eλ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.1917px 7.81667px; transform-origin: 16.1917px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003ef\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.925px 7.81667px; transform-origin: 51.925px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are scalars and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.85px 7.81667px; transform-origin: 36.85px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a vector.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.775px; text-align: left; transform-origin: 383.5px 10.775px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93.8px 7.81667px; transform-origin: 93.8px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the output sinusoid\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.375px 7.81667px; transform-origin: 75.375px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the inputs below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 62.95px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.5px 31.475px; transform-origin: 390.5px 31.475px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.9833px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.5px 10.4917px; text-align: left; transform-origin: 362.5px 10.4917px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 27.9167px 7.81667px; transform-origin: 27.9167px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elambda -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eλ\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.9833px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.5px 10.4917px; text-align: left; transform-origin: 362.5px 10.4917px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 64.7667px 7.81667px; transform-origin: 64.7667px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - maximum value of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.9833px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.5px 10.4917px; text-align: left; transform-origin: 362.5px 10.4917px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 78.1667px 7.81667px; transform-origin: 78.1667px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - number of elements in\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.775px; text-align: left; transform-origin: 383.5px 10.775px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.8px 7.81667px; transform-origin: 26.8px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAssume\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.5417px 7.81667px; transform-origin: 19.5417px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 19.5417px 8.375px; transform-origin: 19.5417px 8.375px; \"\u003eA = 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.9583px 7.81667px; transform-origin: 13.9583px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.5417px 7.81667px; transform-origin: 19.5417px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 19.5417px 8.375px; transform-origin: 19.5417px 8.375px; \"\u003ef = 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.6417px 7.81667px; transform-origin: 39.6417px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e . The vector\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.017px 7.81667px; transform-origin: 115.017px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should be linearly spaced from 0 to\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.3083px 7.81667px; transform-origin: 17.3083px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.23333px 7.81667px; transform-origin: 2.23333px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.90833px 7.81667px; transform-origin: 3.90833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.0583px 7.81667px; transform-origin: 34.0583px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e elements.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = damped_cos(lambda, T, N)\r\n  y = lambda + T + N;\r\nend","test_suite":"%%\r\nfiletext = fileread('damped_cos.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n%%\r\ny_correct = [1.0000 0.7246 0.1554 -0.4232 -0.7524 -0.7118 -0.3583 0.1177 0.4912 0.6065];\r\ny_test = damped_cos(0.5, 1, 10);\r\nassert( all ( abs(y_correct(:) - y_test(:)) \u003c 1e-4 ) )\r\n%% \r\ny_correct = [1.0000 -3.4903 12.1825];\r\ny_test = damped_cos(-0.5, 5, 3)\r\nassert( all ( abs(y_correct(:) - y_test(:)) \u003c 1e-4 ) )","published":true,"deleted":false,"likes_count":64,"comments_count":8,"created_by":162851,"edited_by":223089,"edited_at":"2024-09-14T15:42:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11290,"test_suite_updated_at":"2024-09-14T15:42:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-08-19T15:55:21.000Z","updated_at":"2026-04-11T17:44:21.000Z","published_at":"2019-08-29T18:09:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe equation of a damped sinusoid can be written as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = A.ⅇ^(-λt)*cos(2πft)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eλ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are scalars and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the output sinusoid\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e given the inputs below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elambda -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eλ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - maximum value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - number of elements in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . The vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should be linearly spaced from 0 to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, with\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 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