What is the inverse of y=pi/2+sin x

Question

asked Aug 16, 2020 132k views

2 Answers

Tinychen · Answer 1 · 2020-08-22T22:30:07+0000

Answer:

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

Explanation:

The given function is

$y=(\pi)/(2)+\sin x$

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

$x=(\pi)/(2)+\sin y$

we now solve for y.

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

Take the sine inverse of both sides to obtain;

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

Hence the inverse of the given function is;

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

where
$(\pi)/(2)-1\le x\le (\pi)/(2)+1$