Trig Angles tan2x

Quote:

Originally Posted by skeske1234

If cosx=-3/5 and pi<x<3pi/2, find tan2x

I got tan2x=-16/7

Is my answer right? or is it tan2x=-24/7?

Hi skeske1234,

Actually, I got $\tan 2x=\frac{24}{7}$

If $\cos x =-\frac{3}{5}$ , then $x=-3$ and $r=5$ and $y=4$

So, $\tan x=-\frac{4}{3}$

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

$\tan 2x=\frac{2(-\frac{4}{3})}{1-(-\frac{4}{3})^2}$

$\tan 2x = \frac{2(-\frac{4}{3})}{1-\frac{16}{9}}$

$\tan 2x = \frac{-\frac{8}{3}}{-\frac{7}{9}}$

$\tan 2x = \frac{24}{7}$