Question

Solving for theta? `1/2 = cos^2(2*pi*sin(theta))`

So apparently I have forgotten all of my undergrad maths, trying to solve the following equation for theta `1/2 = cos^2(2*pi*sin(theta))` .

I know it must be an identity I have forgotten, but I cannot seem to find it online.

Answer 1

`theta=7.18^@, 22.02^@, 38.68^@, 61.05^@`

Explanation:

.

`1/2=cos^2(2pisintheta)`

Let's let `2pisintheta=x`:

`1/2=cos^2x`

`cosx=+-sqrt2/2`

`x=arccos(+-sqrt2/2)=pi/4, (3pi)/4, (5pi)/4, (7pi)/4`

`2pisintheta=pi/4, (3pi)/4, (5pi)/4, (7pi)/4`

`sintheta=1/8, 3/8, 5/8, 7/8`

`theta=arcsin(1/8, 3/8, 5/8, 7/8)`

`theta=7.18^@, 22.02^@, 38.68^@, 61.05^@`