Solving trigonometric equation using "solve" function.

Hi,

I'm trying to solve trigonometric equation as follows,

230.769*cos(x) + 153.846*sin(x) =1.715.

For this, I'm using the matlab code,

syms x;

solve(230.769*cos(x)+153.846*sin(x) == 1.715, x, 'IgnoreProperties',true, 'ReturnConditions', true);

but, in the answer structure, I couldn't find the values. The ans.x field shows that it hase 2 symbols, but there isn't any value inside them. Can you please help to find what is wrong?

Thank you.

Answer 1

[John D'Errico]

Whats the problem? There is no need to set any properties anyway on such a trivial problem.

syms x;
x = solve(230.769*cos(x)+153.846*sin(x) == 1.715, x);
vpa(x)
ans =
                                             2.1526153643152832650062014581097
 - 0.97661015722014818434287396730445 - 1.8367099231598242312011508394098e-40i

The second solution is real, it just has an infinitesimal imaginary part.

And of course, you can add any multiple of 2*pi to those solutions.

But even if you do as you did, then LOOK AT THE SOLUTION THAT YOU DID GET. THINK ABOUT IT!

xsol = solve(230.769*cos(x)+153.846*sin(x) == 1.715, x, 'IgnoreProperties',true, 'ReturnConditions', true)
xsol = 
  struct with fields:

             x: [2×1 sym]
    parameters: [1×1 sym]
    conditions: [2×1 sym]
>> vpa(xsol.x)
ans =
                                             6.283185307179586476925286766559*k + 2.1526153643152832650062014581097
 6.283185307179586476925286766559*k - (0.97661015722014818434287396730445 + 1.8367099231598242312011508394098e-40i)

Which says that for integer k, you can add any integer multiple of 2*pi to the solution. I'm pretty sure I said that initially.

xsol.conditions
ans =
 in(k, 'integer')
 in(k, 'integer')

[Biswajit Dipan Biswas]

Thank you so much. I didn't know the application of vpa function. I appreciate your prompt help.

Answer 2

[Jaimin amin]

sol=solve({-sin[t2+t3]-sin[t2]==-1.5 && cos[t2+t3]+cos[t2]==0.8660},{t2,t3})

[Jaimin amin]

to find t2 and t3

[Torsten]

syms x y real
sol=solve([sin(x+y)+sin(x)==1.5,cos(x+y)+cos(x)==0.5*sqrt(3)],[x y])

sol = struct with fields:
    x: [2×1 sym]
    y: [2×1 sym]

sol.x

ans = 

sol.y

ans =