Answer to Question #143738 in Trigonometry for Shahir Sheikh

Question

Suppose cos(theta) = -5/13 and tan<0 find sin(2theta)

Answer 1

$Cos\theta=\frac{-5}{13}$

$Cos^2\theta+sin^2\theta=1$

$(\frac{-5}{13})^2+sin^2\theta=1$

$Sin^2\theta=1-\frac{25}{169}$

$Sin^2\theta=\frac{144}{169}$

$Sin\theta=\frac{12}{13}$

$Sin2\theta=2sin\theta cos\theta$

$=2\times \frac{12}{13} \times \frac{-5}{13}$

$Sin2\theta=\frac{-120}{169}$