Please Help Me!!! I have No clue!!! 95 Points!! Explain why sin^(-1) (sin((3\pi )/(4) ))\\eq (3\pi )/(4) when y=sin x and y=sin^(-1) x

Question

Please Help Me!!! I have No clue!!! 95 Points!!

Explain why
`sin^(-1) (sin((3\pi )/(4) ))\\eq (3\pi )/(4)` when y=sin x and
`y=sin^(-1) x`

Answer 1

Explanation:

Double check that you have copied down all of the info given in this problem.

y = sin x and y = arcsin x are inverse functions, period, BUT y = sin x fails the horizontal line test (which is used to determine whether or not a given function has an inverse or not). If you plot this sine function and then draw a horizontal line through it, the line will intersect the graph of the sine function in more than one place. In order for us to find the inverse of the sine function, we must define its domain as [-π/2, π/2].

In this problem, the x-value is 3π/4, which is outside the above domain. For that reason we must reject 3π/4 as a solution.

The sine function and the inverse sine function cancel out (undo) each other, which leaves the argument 3pi/4, which is equivalent to 135 degrees and is in Quadrant II. But for the reason stated immediately above, 3π/4 is NOT a solution.