Answer
(a) $[-1,1] , [-\frac{\pi}{2}, \frac{\pi}{2}]$.
(b) $[-1,1] , [0, \pi]$.
(c) $R , [-\frac{\pi}{2}, \frac{\pi}{2}]$.
Work Step by Step
The sine, cosine, and tangent functions are one-to one only on the restricted domains thus their inverse functions have a closed range as following-
(a) The function $\sin^{-1}$ has domain $[-1,1]$ and range $[-\frac{\pi}{2}, \frac{\pi}{2}]$.
(b) The function $\cos^{-1}$ has domain $[-1,1]$ and range $[0, \pi]$.
(c) The function $\tan^{-1}$ has domain $R$ and range $[-\frac{\pi}{2}, \frac{\pi}{2}]$
