Choose the one alternative that best completes the statement or answers the question.
Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\csc \left( - 30 ^ { \circ } \right)$
A) 2
B) $- \frac { 2 \sqrt { 3 } } { 3 }$
C) $- 2$
D) $\frac { 2 \sqrt { 3 } } { 3 }$

Question

Quizplus · Accepted Answer

The cosecant function, $\csc$, is the reciprocal of the sine function. Since sine is an odd function, $\sin(-\theta) = -\sin(\theta)$. Therefore, $\csc(-30^\circ) = -\csc(30^\circ)$. The value of $\csc(30^\circ)$ is 2, so $\csc(-30^\circ) = -2$.

Choose the One Alternative That Best Completes the Statement or Answers