Find theta angle in complex form

[baby_1]

Homework Statement

Here is my equation that I want to find theta angle

Homework Equations

The Attempt at a Solution

I try to set different value of cos (theta) to find theta but it failed , I want to know the main solving strategy
Thanks

 

[RUber]

What if you were to substitute cos(theta) = x and sin(theta) = y, and enforce the fact that y = sqrt(1-x^2)? Usually these eventually simplify to a quadratic equation to solve--after some work.

 

[baby_1]

Thanks for your replay
I did with the same way:

as I plot these charts I have

It has two roots (+.63,-.63) but the both of them indicate that theta should be 53 degree that is opposite the my books answer that theta should be 12 degree

what is my fault?

 

[BvU]

No fault. I don't get 53 degrees but 50.9612 (cos = 0.629847 so like you found it).
Satisfies your equation.

Looks as if the book answer is wrong.

 

[RUber]

I concur with BvU. 12 degrees does not satisfy the equation.
cos(pi/2*cos( 12 ))/sin( 12 ) = 0.1651,which does not equal sqrt(2)/2 = 0.7071.