# How do you use a double angle identity to find the exact value of each expression?

Mar 6, 2015

You would need an expression to work with.

For example:
Given $\sin \alpha = \frac{3}{5}$ and $\cos \alpha = - \frac{4}{5}$, you could find $\sin 2 \alpha$ by using the double angle identity
$\sin 2 \alpha = 2 \sin \alpha \cos \alpha$.

$\sin 2 \alpha = 2 \left(\frac{3}{5}\right) \left(- \frac{4}{5}\right) = - \frac{24}{25}$.

You could find $\cos 2 \alpha$ by using any of:
$\cos 2 \alpha = {\cos}^{2} \alpha - {\sin}^{2} \alpha$
$\cos 2 \alpha = 1 - 2 {\sin}^{2} \alpha$
$\cos 2 \alpha = 2 {\cos}^{2} \alpha - 1$

In any case, you get $\cos \alpha = \frac{7}{25}$.