# How do you calculate tan(2arcsin(-8/17))?

Jun 21, 2016

$\pm \frac{240}{161}$.

#### Explanation:

Let $a = a r c \sin \left(- \frac{8}{17}\right)$. Then $\sin a = - \frac{8}{17} < 0.$.

So, a is in either 3rd quadrant or in the 4th. Accordingly,

$\cos a = \pm \sqrt{1 - {8}^{2} / {17}^{2}} = \pm \frac{15}{17} \mathmr{and} \tan a = \pm \frac{8}{15}$.

Now, the given expression is

$\tan 2 a = \frac{2 \tan a}{1 - {\tan}^{2} a}$

$= \pm \frac{\frac{16}{15}}{1 - {8}^{2} / {15}^{2}}$

$= \pm \frac{240}{161}$..