Solution:
Given:
f (θ) = 4sin θ + 1
g (θ) = cos 2θ
We want to find the value(s) on the interval [0, 2π) where f (θ) = g (θ).
[tex]\begin{gathered} f(\theta)=g(\theta)\text{ gives } \\ 4sin\theta+1=cos2\theta \\ Recall\text{ that cos2}\theta=1-2sin^2\theta \\ Hence,\text{ } \\ 4sin\theta+1=1-2sin^2\theta \\ 2sin^2\theta+4sin\theta+1-1=0 \\ 2sin^2\theta+4sin\theta=0 \\ factorize\text{ sin}\theta \\ sin\theta(2sin\theta+4)=0 \end{gathered}[/tex][tex]undefined[/tex]
