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

Question

Quizplus · Accepted Answer

The secant function is the reciprocal of the cosine function. For an angle of 240°, which is in the third quadrant where cosine is negative, we can find the reference angle to be 60°. The cosine of 60° is $ \frac{1}{2} $, so the secant (being the reciprocal) is $ \frac{1}{\cos(240^\circ)} = -2 $, because cosine is negative in the third quadrant.

Evaluate Without Using a Calculator by Using Ratios in a Reference