Solve the problem.
-If $\cos \theta = - \frac { 5 } { 13 }$, and $\theta$ terminates in quadrant II, then find $\cos 2 \theta$.
A) $- \frac { 120 } { 169 }$

B) $\frac { 120 } { 169 }$

C) $\frac { 119 } { 169 }$

D) $- \frac { 119 } { 169 }$

Question

Solve the problem.
-If $\cos \theta = - \frac { 5 } { 13 }$, and $\theta$ terminates in quadrant II, then find $\cos 2 \theta$.
A) $- \frac { 120 } { 169 }$

B) $\frac { 120 } { 169 }$

C) $\frac { 119 } { 169 }$

D) $- \frac { 119 } { 169 }$

Quizplus · Accepted Answer

In quadrant II, sine is positive. Using $\sin^2 \theta + \cos^2 \theta = 1$, $\sin \theta = \frac{12}{13}$. Then, $\cos 2\theta = 2\cos^2 \theta - 1 = 2\left(-\frac{5}{13}\right)^2 - 1 = -\frac{119}{169}$.

Solve the Problem cos⁡θ=−513\cos \theta = - \frac { 5 } { 13 }cosθ=−135​

Solve the Problem $\cos \theta = - \frac { 5 } { 13 }$