Use identities to write each expression as a function of .
-Find $\csc \theta$ if $\cot \theta = - \sqrt { 15 }$ and $\theta$ is in quadrant II.
A) 4
B) $- \frac { 1 } { 4 }$
C) $\frac { 1 } { 4 }$
D) $- 4$

Question

Quizplus · Accepted Answer

In quadrant II, both $\csc \theta$ and $\cot \theta$ are negative. Given $\cot \theta = - \sqrt { 15 }$, we can use the identity $\csc^2 \theta = 1 + \cot^2 \theta$ to find $\csc \theta$. Substituting $\cot \theta = - \sqrt { 15 }$ into the identity gives $\csc^2 \theta = 1 + 15 = 16$, so $\csc \theta = \pm 4$. Since $\theta$ is in quadrant II where $\csc \theta$ is positive, $\csc \theta = 4$.

Use Identities to Write Each Expression as a Function of csc⁡θ\csc \thetacscθ

Use Identities to Write Each Expression as a Function of $\csc \theta$