Use the fundamental identities to find the value of the trigonometric function.
-Find $\cos \theta$, given that $\sin \theta = - \frac { 5 } { 13 }$ and $\theta$ is in quadrant III.
A) $- \frac { 5 } { 12 }$
B) $\frac { 12 } { 5 }$
C) $- \frac { 13 } { 5 }$
D) $- \frac { 12 } { 13 }$

Question

Quizplus · Accepted Answer

In quadrant III, both sine and cosine are negative. Using the Pythagorean identity $\sin^2\theta + \cos^2\theta = 1$, we find $\cos\theta = -\sqrt{1 - \sin^2\theta} = -\sqrt{1 - \left(-\frac{5}{13}\right)^2} = -\frac{12}{13}$.

Use the Fundamental Identities to Find the Value of the Trigonometric