Use reference angles to find the exact value of the expression. Do not use a calculator.
-$\csc 660 ^ { \circ }$
A) $- \frac { 2 \sqrt { 3 } } { 3 }$
B) $- \sqrt { 2 }$
C) $- \sqrt { 3 }$
D) $- \frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The csc function is the reciprocal of the sin function. To find the exact value of csc(660°), first find the reference angle. 660° - 360° = 300°, which has a reference angle of 60°. The sin(60°) = $\sqrt{3}/2$, so csc(60°) = 2/$\sqrt{3}$. To rationalize, multiply by $\sqrt{3}/\sqrt{3}$ to get $2\sqrt{3}/3$. Since 300° is in the fourth quadrant where csc is negative, the answer is $-2\sqrt{3}/3$.

Use Reference Angles to Find the Exact Value of the Expression