Question

From the crests of `y = sin x, 1 = sin (pi/2) = sin ((5/2)pi) = sin ((9/2)pi) = ...` How do you evaluate `sin^(-1) sin (pi/2), sin^(-1) sin ((5/2)pi), sin^(-1) sin ((9/2)pi), ...?`

Answer 1

`sin^(-1)sinx=x`

Explanation:

Arcsine of sine of a quantity is the same quantity back again. So `sin^(-1)sin(pi/2)=pi/2`, etc.

Note that the notation `sin^(-1)x` is used to mean the inverse function of sine (i.e. arcsine).