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) $- \frac { 12 } { 13 }$
D) $- \frac { 13 } { 5 }$

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 can solve for $\cos \theta$. Given $\sin \theta = -\frac{5}{13}$, we have $(- \frac{5}{13})^2 + \cos^2 \theta = 1$. Solving for $\cos \theta$, we find $\cos \theta = -\frac{12}{13}$.

Use the Fundamental Identities to Find the Value of the Trigonometric