Question

How do you evaluate `sin^-1(sin(-(pi)/10))`?

Answer 1

`sin^-1 (sin(-pi/10))=-pi/10`

Explanation:

`sin^-1 (sin(-pi/10))`

The restriction for the range of `sin^-1x` is `[-pi/2,pi/2]` and since `-pi/10` is in the range we can apply the property `f^-1(f(x)=x`. That is,
`sin^-1 (sin(-pi/10))=-pi/10`