Evaluate without using a calculator by using ratios in a reference triangle.
-$\cos 210 ^ { \circ }$
A) $- \frac { \sqrt { 3 } } { 2 }$
B) $\frac { \sqrt { 2 } } { 2 }$
C) $- \frac { \sqrt { 2 } } { 2 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

To evaluate $\cos 210^\circ$, we can use the unit circle or reference triangles. $210^\circ$ is in the third quadrant where both sine and cosine are negative. It corresponds to a reference angle of $30^\circ$ because $210^\circ - 180^\circ = 30^\circ$. The cosine of a $30^\circ$ angle is $\frac{\sqrt{3}}{2}$, but since $210^\circ$ is in the third quadrant where cosine is negative, $\cos 210^\circ = -\frac{\sqrt{3}}{2}$.

Evaluate Without Using a Calculator by Using Ratios in a Reference