Inverse Circular Functions and Principal Values

The inverse circular functions use their principal values. The superscript \(-1\) in an inverse-function name does not mean a reciprocal.

\(y=\arcsin x\): \(-1\le x\le1\), \(-\frac\pi2\le y\le\frac\pi2\).

\(y=\arccos x\): \(-1\le x\le1\), \(0\le y\le\pi\).

\(y=\arctan x\): \(x\in\mathbb R\), \(-\frac\pi2<y<\frac\pi2\).

For example, \(\arccos(0)=\frac\pi2\), whereas \(\frac1{\cos0}=1\). State a restricted domain when a composite inverse function is differentiated.