Use the fundamental identities to find the value of the trigonometric function.
-Find $\csc \theta$, given that $\cot \theta = - \sqrt { 3 }$ and $\theta$ is in quadrant II.
A) $- 2$
B) 2
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

In quadrant II, sine is positive. Since $\cot \theta = -\sqrt{3}$, $\tan \theta = -\frac{1}{\sqrt{3}}$. Using $\sin^2 \theta + \cos^2 \theta = 1$ and $\tan \theta = \frac{\sin \theta}{\cos \theta}$, solve for $\sin \theta = \frac{\sqrt{3}}{2}$. Thus, $\csc \theta = \frac{1}{\sin \theta} = 2$.

Use the Fundamental Identities to Find the Value of the Trigonometric