AP Precalculus / Unit 3: Trigonometric and Polar Functions
3.9 Inverse Trigonometric Functions
Notes
With restricted domains:
- $\arcsin x$: range $\displaystyle \left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.
- $\arccos x$: range $[0,\pi]$.
- $\arctan x$: range $\displaystyle \left(-\frac{\pi}{2},\frac{\pi}{2}\right)$.
Practice
$\displaystyle \arcsin\frac{1}{2}=$
In radians, within the range.
$\arccos(-1)=$
$\cos\pi=-1$.
Why are trig domains restricted for inverses?
A function needs to be one-to-one to have an inverse.
Ready for more? Take the Unit 3 test.