Question

How do you solve and find the value of `sin^-1(tan(pi/4))`?

Answer 1

`sin^(-1)(tan(pi/4))=color(green)(pi/2+k * 2pi,AAk in ZZ)`

Explanation:

The angle `pi/4` is one of the standard angles with
`color(white)("XXX")tan(pi/4)=1`

So `sin^(-1)(tan(pi/4))=sin^(-1)(1)`

If we restrict `theta` to the range `[0,2pi)`
the only value of `theta` for which `sin(theta)=1` is `theta=pi/2`

For the unrestricted case, this value will repeat with every complete rotational cycle,
so `theta=pi/2+k * 2pi, AAkinZZ`