# How do you find sin 2θ, given cos θ = 5/13 and θ lies in Quadrant IV?

Nov 18, 2015

Find sin 2x, knowing $\cos x = \frac{5}{13}$

Ans: $- \frac{120}{169}$

#### Explanation:

$\cos x = \frac{5}{13.}$ Find sin x.
${\sin}^{2} x = 1 - {\cos}^{2} x = 1 - \frac{25}{169} = \frac{144}{169}$ --> $\sin x = \pm \frac{12}{13}$.
Since x is in Quadrant IV, then sin x is negative.
$\sin x = - \frac{12}{13}$.
$\sin 2 x = 2 \sin x . \cos x = 2 \left(- \frac{12}{13}\right) \left(\frac{5}{13}\right) = - \frac{120}{169}$