Question

How do you find the exact value of `sin(tan^-1 -5/7)`?

Answer 1

`-5/sqrt74`

Explanation:

`tan^(-1)(-5/7)= sin^(-1)(-5/sqrt(5^2+7^2))=sin^(-1)(-5/sqrt74)`

The given expression is

`sin(sin^(-1)(-5/sqrt74))=-5/sqrt74`.

Note that , if arc tan is negative, the angle is in `Q_4`, and so,

`arc sin in Q_4` is also negative.