Chapter 1.7, Problem 29ES

The function ${\cot }^{-1}x$ is defined to be the inverse of the restricted cotangent function $\cot x,0<x<\pi$ and the function ${\csc }^{-1}x$ is defined to be the inverse of the restricted cosecant function $\csc x,-\pi /2\le x\le \pi /2,x\ne 0$ Use these definitions in these and in all subsequent exercises that involve these functions.

(a) Sketch the graphs of ${\cot }^{-1}x$ and ${\csc }^{-1}x$ .

(b) Find the domain and range of ${\cot }^{-1}x$ and ${\csc }^{-1}x$ .