Why arcsin Gives One Angle

The line at height 1/2 meets the sine wave again and again: $\sin\left(30^{\circ}\right)$, $\sin\left(150^{\circ}\right)$ and $\sin\left(390^{\circ}\right)$ are all 1/2. arcsin(c) means the angle whose sine is c. It must give one answer, so it uses one part of the wave.

From −90° to 90°, the sine goes from −1 up to 1 and meets each value once. These angles are arcsin's range: the only angles it gives back. So a negative input gives a negative angle: $\arcsin\left(\frac{-1}{2}\right) = -30^{\circ}$, never 330°.