Use the fundamental identities to find the value of the trigonometric function.
-Find $\csc \theta$, given that $\cot \theta = - \sqrt { 15 }$ and $\theta$ is in quadrant II.
A) $\frac { 1 } { 4 }$
B) $- \frac { 1 } { 4 }$
C) $- 4$
D) 4

Question

Quizplus · Accepted Answer

In quadrant II, sine is positive, so cosecant (which is the reciprocal of sine) is also positive. Given $\cot \theta = -\sqrt{15}$, we can use the identity $\cot^2 \theta + 1 = \csc^2 \theta$ to find $\csc \theta$. Plugging in the given value, we get $(- \sqrt{15})^2 + 1 = \csc^2 \theta$, which simplifies to $15 + 1 = 16 = \csc^2 \theta$. Taking the square root gives $\csc \theta = 4$, since we're looking for the positive value in quadrant II.

Use the Fundamental Identities to Find the Value of the Trigonometric