Functions, graphs and inverses practice question 11

Read $\sin x$ as a single unknown. What kind of equation is that, and how many angles in $[0, 2\pi)$ can share one value of sine?

The equation is a quadratic in $\sin x$. Factor it as you would $2u^{2} - u - 1$.

Each value of $\sin x$ gives its own solutions. Draw the unit circle and count them: $\sin x = -\tfrac{1}{2}$ has two in $[0, 2\pi)$.