Question

Write the equation for the inverse of the function y = pi/4 + sin x.

Answer 1

Isolate x

Answer 2

To find the inverse function, replace x with y and y with x and then solve for y.

Answer 3

I've got that far, I just don't know how to solve for y once I get there. I got x = arcsin (y - pi/4)

Answer 4

y = pi/4 + sin x
To find the inverse function, First step: replace x with y and y with x
x = pi/4 + sin(y)
solve for y.
subtract pi/4 from both sides
x - pi/4 = sin(y)
take arcsin on both sides
arcsin(x-pi/4) = y
y = arcsin(x-pi/4) is the inverse function.

Answer 5

Or in your answer you can replace x with y and y with x and you will get the same answer. You are doing the interchange as a last step. I prefer interchanging x and y as the first step in finding the inverse.

Answer 6

thank you guys for the help

Answer 7

you are welcome.