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. The sine function is odd, meaning $\sin(-\theta) = -\sin(\theta)$. Therefore, $\csc(-30^\circ) = -\csc(30^\circ)$. Since $\csc(30^\circ) = 2$, it follows that $\csc(-30^\circ) = -2$.

Use the Even-Odd Properties to Find the Exact Value of the Expression