Find theta angle in complex form

In summary, the conversation discusses finding the theta angle using the equation cos(theta) = x and sin(theta) = y, and suggests substituting values to eventually solve a quadratic equation. The book's answer of 12 degrees is incorrect, with the correct answer being approximately 50.9612 degrees.
  • #1
baby_1
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Homework Statement


Here is my equation that I want to find theta angle
gif.gif


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
 
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  • #2
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.
 
  • #3
Thanks for your replay
I did with the same way:
%7B2%7D%5Ccos%28%5Ctheta%29%29%7D%7B%5Csin%28%5Ctheta%29%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D.gif

D%7B2%7D%5Ccos%28%5Ctheta%29%29%3D%5Csin%28%5Ctheta%29%3D%5Csqrt%7B1-%5Ccos%5E2%28%5Ctheta%29%7D.gif

gif.gif

gif.gif

as I plot these charts I have
file.jpg


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?
 
  • #4
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.
 
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  • #5
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.
 
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1. What is a theta angle in complex form?

A theta angle in complex form is an angle that represents a complex number in the polar form, which is expressed in terms of its magnitude (or modulus) and angle (or argument).

2. How do you find the theta angle in complex form?

To find the theta angle in complex form, you can use the inverse tangent function, also known as arctangent, on the imaginary and real parts of the complex number. The resulting angle is the theta angle in radians.

3. Can the theta angle in complex form be negative?

Yes, the theta angle in complex form can be negative. It depends on the quadrant in which the complex number is located on the complex plane. In the first and fourth quadrants, the theta angle is positive, while in the second and third quadrants, it is negative.

4. Why is it important to find the theta angle in complex form?

The theta angle in complex form is important because it helps us understand the magnitude and direction of a complex number. It is also used in operations such as multiplication and division of complex numbers.

5. Can a complex number have multiple theta angles in complex form?

Yes, a complex number can have multiple theta angles in complex form. This is because the theta angle is not unique and can have different values depending on the branch of the complex plane. To avoid confusion, mathematicians usually use the principal value of theta angle, which lies between -π and π radians.

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