Meaning imaginary result of asin(x) function of MATLAB
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Dear all,
I have a question about asin(x) function of MATLAB. As we know from the mathematics, if the argument of arcsin(x) function (e.g. x) is bigger than one, then this function MUST not have any answer. For example, if we calculate arcsin(1.5) with calculator, there is error in the calculator which is obvious and completely clear, but when we write in MATLAB: asin(1.5) it gives us an imaginary result equal to 1.5708 - 0.9624i
My question is how can we interpret this imaginary number? Does it have any meaning? Why does MATLAB give us imaginary answer, while we expect to see error answer by MATLAB?
Before all, I want to thank you for helping me to interpret this imaginary numbers by MATLAB if they have any meaning.
It would be my pleasure, if you can provide me any referrence for your answer also.
I am looking forward to hearing from you. Thank you so much for your time and considerations.
Best regards,
Hadi
4 comentarios
John D'Errico
el 13 de Mayo de 2019
"As we know from mathematics" - this may just indicate one needs to know more mathematics. In this case, it is about the extension of the trig functions to the complex plane.
Respuestas (1)
Stephen23
el 13 de Mayo de 2019
Editada: Stephen23
el 13 de Mayo de 2019
"'My question is how can we interpret this imaginary number? Does it have any meaning?
Yes, it has a meaning.
Why does MATLAB give us imaginary answer, while we expect to see error answer by MATLAB?"
I don't expect to get an error, because as we all know, trigonometric functions can be easily extended to the complex domain:
All your example shows is that sin(1.5708 - 0.96242i) == 1.5
If you really want, you can easily calculate this yourself, using the various identities of trigonometric functions on the complex plane:
>> y = 1.5;
>> x = -i*log(y*i+sqrt(1-y^2)) % == arcsine
x = 1.57080 - 0.96242i
2 comentarios
John D'Errico
el 13 de Mayo de 2019
Special meaning? They mean exactly what the absolute value and phase of any complex number mean. What would you think is special?
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