Getting Triggy With It #2

When the two functions intersect, we have:

$\begin{aligned} \sin 2x & = \cos x \\ 2 \sin x \cos x - \cos x & = 0 \\ \cos x (2\sin x - 1) & = 0 \end{aligned}$

$\implies \begin{cases} \cos x = 0 & \implies \dfrac \pi 2, \dfrac 32 \pi, \dfrac 52 \pi \\ \sin x = \dfrac 12 & \implies \dfrac \pi 6, \dfrac 56 \pi, \dfrac {13}6 \pi, \dfrac {17}6 \pi \end{cases}$

Therefore, the two functions intersect $\boxed 7$ times in $[0, 3\pi]$ .