Evaluate without using a calculator by using ratios in a reference triangle.
-$\tan 300 ^ { \circ }$
A) $\sqrt { 3 }$
B) $- \sqrt { 3 }$
C) $- \frac { \sqrt { 3 } } { 3 }$
D) $\frac { \sqrt { 3 } } { 3 }$

Question

Quizplus · Accepted Answer

The tangent of an angle in standard position is the ratio of the y-coordinate to the x-coordinate of a point on the terminal side of the angle. For $\tan 300^\circ$, this angle is in the fourth quadrant where tangent values are negative. The reference angle for $300^\circ$ is $60^\circ$, and $\tan 60^\circ = \sqrt{3}$. Therefore, $\tan 300^\circ = -\sqrt{3}$.

Evaluate Without Using a Calculator by Using Ratios in a Reference