Use the fundamental identities to find the value of the trigonometric function.
-Find $\sin \theta$ if $\cos \theta = \frac { 5 } { 6 }$ and $\theta$ is in quadrant IV.
A) $\frac { \sqrt { 33 } } { 4 }$
B) $\frac { 5 \sqrt { 29 } } { 29 }$
C) $- \frac { \sqrt { 11 } } { 6 }$
D) $\frac { 4 } { 5 }$

Question

Quizplus · Accepted Answer

In quadrant IV, sine is negative, and using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$, we find $\sin \theta = -\sqrt{1 - \cos^2 \theta} = -\sqrt{1 - \left(\frac{5}{6}\right)^2} = -\frac{\sqrt{11}}{6}$.

Use the Fundamental Identities to Find the Value of the Trigonometric