Question

How do you evaluate `sin^-1(sin((3pi)/10))`?

Answer 1

`(3pi)/10`.

Explanation:

Let us recall the Defn. of `sin^-1` fun. :

`sin^-1x=theta, |x| le1 iff sintheta=x, theta in [-pi/2,pi/2]`

`:. sin^-1(sintheta)=theta, AAtheta in [-pi/2,pi/2].`

In our case. since, `3pi/10 in [-pi/2,pi/2], sin^-1(sin((3pi)/10)=(3pi)/10`.