Question

find the exact value of the expression
sin^-1(sin3pi/4)

Answer 1

pi/12

Answer 2

they usually restrict sine to the interval [-pi/2, pi/2] so that it's one to one and invertible. this means that the range of inverse sine will also be [-pi/2, pi/2].

so the answer won't be 3pi/4, but rather a value y such that sin(y) = sin(3pi/4), where y is in the interval [-pi/2, pi/2], which will be pi/4