Question

Find all solutions to the following equations that are on the interval [0,2pie] by solving for theta

Answer 1

Given:

$cos(2\theta)sin(\theta)+sin(\theta)=0$

let us take the common term out,

$\begin{gathered} sin(\theta)(cos(2\theta)+1)=0 \\ \end{gathered}$

Now, let us solve seperately,

$\begin{gathered} \sin (\theta)=0 \\ \theta=2\pi n \end{gathered}$

$\begin{gathered} \cos (2\theta)+1=0 \\ \theta=\frac{\pi}{2}+\pi n \end{gathered}$

The solutions are,

$\theta=2\pi n,\: \theta=\pi+2\pi n,\: \theta=\frac{\pi}{2}+\pi n$