Question

Find solutions for sinθ=cos2θ

Answer 1

A solution using Mathematica 9 is attached.

Answer 2

Given
sinθ=cos2θ , we have
Left= \[\sin \theta=\cos ^{2} \theta-\sin ^{2} \theta=1-2\sin ^{2} \theta\] =Right,

So, let x=sinθ,
\[2x ^{2}+x-1=0\]
x1=-1,x2=1/2;
So,
1. If sinθ=-1,
\[\theta=\frac{ 3 }{ 2 }θ+2(\pi)k, k=Z;\]
2. If sinθ=1/2,
\[\theta=\frac{1 }{4 }θ+2(\pi)k, k=Z;\]