Practice Inverse Trigonometric Functions in Math

Quick Recap

Functions that reverse the trigonometric functions: given a ratio, they return the corresponding angle. $\arcsin$, $\arccos$, and $\arctan$ are the inverses of $\sin$, $\cos$, and $\tan$ on restricted domains.

Regular trig functions answer: 'Given an angle, what's the ratio?' Inverse trig functions answer the reverse: 'Given a ratio, what's the angle?' Since $\sin$ and $\cos$ are many-to-one (many angles give the same ratio), we must restrict their domains to make the inverse a proper function. Think of it like this: if you know the slope of a ramp is $0.5$, $\arcsin (0.5)=30\mathrm{°}$ tells you the angle.