Use the fundamental identities to find the value of the trigonometric function.
-Find $\cot \theta$ if $\sec \theta = - \frac { \sqrt { 53 } } { 7 }$ and $\theta$ is in quadrant II.
A) $\frac { 2 } { 7 }$

B) $\frac { \sqrt { 53 } } { 2 }$

C) $- \frac { 7 } { 2 }$

D) $- \frac { \sqrt { 53 } } { 2 }$

Question

Use the fundamental identities to find the value of the trigonometric function.
-Find $\cot \theta$ if $\sec \theta = - \frac { \sqrt { 53 } } { 7 }$ and $\theta$ is in quadrant II.
A) $\frac { 2 } { 7 }$

B) $\frac { \sqrt { 53 } } { 2 }$

C) $- \frac { 7 } { 2 }$

D) $- \frac { \sqrt { 53 } } { 2 }$

Quizplus · Accepted Answer

In quadrant II, cosine is negative, so $\cos \theta = -\frac{7}{\sqrt{53}}$. Using $\sin^2 \theta + \cos^2 \theta = 1$, find $\sin \theta = \frac{2}{\sqrt{53}}$. Then, $\cot \theta = \frac{\cos \theta}{\sin \theta} = -\frac{7}{2}$.

Use the Fundamental Identities to Find the Value of the Trigonometric