Evaluate without using a calculator by using ratios in a reference triangle.
-$\csc 240 ^ { \circ }$
A) $- \frac { 2 \sqrt { 3 } } { 3 }$
B) $- 2$
C) $\frac { 2 \sqrt { 3 } } { 3 }$
D) 2

Question

Quizplus · Accepted Answer

$\csc 240^\circ$ corresponds to the reciprocal of the sine function in the third quadrant, where sine is negative. Since $\sin 240^\circ = -\frac{\sqrt{3}}{2}$, $\csc 240^\circ = -\frac{2}{\sqrt{3}}$, which simplifies to $-\frac{2\sqrt{3}}{3}$ when rationalized.

Evaluate Without Using a Calculator by Using Ratios in a Reference