Question

What is the inverse of y=pi/2+sin x​

Answer 1

what that guy said

Explanation:

Answer 2

`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`