5.1 Inverse Functions and Restricted Domains

Notes

Sine, cosine and tangent repeat, so they fail the horizontal line test. To get inverses we restrict the domain to one piece where each function is one-to-one.

• $y = \arcsin x$ (also $\sin^{-1}x$): domain $[-1, 1]$, range $\displaystyle \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.
• $y = \arccos x$: domain $[-1, 1]$, range $[0, \pi]$.
• $y = \arctan x$: domain all real numbers, range $\displaystyle \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.
• The output of an inverse trig function is an angle.