Explain why sin^-1(sin(3pil4)) is not equal to 3pi/4 when y=sin x and y=sin^-1x are inverses
When y = sin x and y = sin^(-1)x are inverses, it means that sin(sin^(-1)x) = x for all x in the domain of sin^(-1)x and sin(sin^(-1)x) = x for all x in the domain of sin x.
In this case, sin^(-1)(sin(3 pi/4)) = 3 pi/4 and sin( sin^(-1)(3 pi/4)) = 3 pi/4. This is because sin(3 pi/4) = sqrt(2)/2 which falls within the range of sin^(-1)x, so the inverse function can correctly retrieve the original input.
Therefore, sin^(-1)(sin(3 pi/4)) = 3 pi/4, illustrating that the given expression is correct because of the properties of inverse trigonometric functions.