Question

2sin2theta=1/2, find the value of theta

Answer 1

use
first sin2(theta)=2sin(theta)cos(theta)
then use euler's formula

Answer 2

\[cosx=\frac{ e ^{ix}+e ^{-ix} }{ 2 }\]
\[sinx=\frac{ e ^{ix}-e ^{-ix} }{ 2i}\]
use them

Answer 3

\[2\sin (2\theta)=1/2\Rightarrow \sin (2\theta)=1/4\Rightarrow\\
\Rightarrow 2\theta=\arcsin(1/4)\Rightarrow \theta=\frac{1}{2}\arcsin(1/4)\]