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

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Answer 1 · 2017-01-13T11:02:25

$-5/sqrt74$

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

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.

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