What is the inverse of y=cos(x-pi/2)

Question

asked Jan 1, 2020 207k views

2 Answers

Borjovsky · Answer 1 · 2020-01-06T00:59:22+0000

Answer:

$f^(-1)(x)=\cos^(-1) x+(\pi)/(2)$

Explanation:

The given function is

$y=\cos(x-(\pi)/(2))$

To find the inverse of this function, we interchange x and y.

$x=\cos(y-(\pi)/(2))$

Take the inverse cosine of both sides to obtain;

$\cos^(-1) x=y-(\pi)/(2)$

$\cos^(-1) x+(\pi)/(2)=y$

Therefore the inverse of the given cosine function is;

$f^(-1)(x)=\cos^(-1) x+(\pi)/(2)$ where
$-1\le x\le 1$