Question

Evaluate tan(sin^-1 (-4/5))

Answer 1

$\theta=\sin ^{-1}\left(-\dfrac{4}{5} \right )$ is in the fourth quadrant. Hence,

$\tan \theta$


From a right triangle (check out the attachment) we get

$\bullet\;\;\cos \theta=\dfrac{3}{5}\\\\\\ \bullet\;\;\tan \theta=-\dfrac{4}{3}\\\\\\\\ \therefore~~\boxed{\begin{array}{c} \tan\left(\sin^{-1} \left(-\dfrac{4}{5} \right )\right)=-\dfrac{4}{3} \end{array}}$