4950 The function cot1 x is defined to be the inverse ofthe restricted cotangent

Chapter 0, Problem 49

(choose chapter or problem)

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 \(\csc x,-\pi / 2<x<\pi / 2, x \neq 0\).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 \(\csc ^{-1} x\).

Equation Transcription:

Text Transcription:

cot^-1 ⁡x

cot x,0<x<pi

csc^-1 x

csc x,-pi/2<x<pi/2, x not =0