For how many values of $\theta$ such that $0<\theta<360$ do we have $\cos \theta = 0.1$? (Note that $\theta$ is a measure in radians, not degrees!)
The period of $\cos(x)$ is $2\pi,$ $114pi = 358.14,$ so $\cos(x)$ repeats $114/2 = 57$ times. So the answer is $57 \cdot 2 = 114,$ but since cosine is split over y axis on the first period, we add $1$ to $114,$ and get $115.$
Is my answer correct? Thanks for any confirmation or correction!