# What is Sin( inverse COS 3/5)?

Sep 14, 2015

$\frac{4}{5}$

#### Explanation:

Let inverse $\cos \left(\frac{3}{5}\right)$= $\theta$, so that it is ${\cos}^{-} 1 \left(\frac{3}{5}\right) = \theta$

That means $\cos \theta = \frac{3}{5}$.

Now work out $\sin \theta = \sqrt{1 - {\cos}^{2} \theta} = \frac{4}{5}$

$\theta = {\sin}^{-} 1 \left(\frac{4}{5}\right)$

$\sin {\cos}^{-} 1 \left(\frac{3}{5}\right) = \sin {\sin}^{-} 1 \left(\frac{4}{5}\right) = \frac{4}{5}$