Using principal value, evaluate the following: `sin^(-1)(sin ((3pi)/5))`

Explanation

Principal value of `sin theta` is between `-pi/2 and pi/2`.

`sin^-1(sin((3pi)/5))`

`= sin^-1(sin(pi - (2pi)/5))`

`= sin^-1(sin ((2pi)/5))`

`=(2pi)/5`

As, `((2pi)/5)` is between `-pi/2 and pi/2`, it is the required principal value.