Evaluate the tangent of the angle without using a calculator. $- 300 ^ { \circ }$
A) $\sqrt { 3 }$
B) $- \frac { \sqrt { 3 } } { 3 }$
C) $\frac { \sqrt { 3 } } { 3 }$
D) $\frac { 1 } { 2 }$
E) 0

Question

Quizplus · Accepted Answer

To find the tangent of an angle in degrees, we need to use the formula $	an (	heta) = \frac{\sin(	heta)}{\cos(	heta)}$.

We know that $\sin(-300^{\circ}) = -\frac{1}{2}$ and $\cos(-300^{\circ}) = \frac{\sqrt{3}}{2}$, as $-300^{\circ}$ is in the fourth quadrant.

Then, we have: 
$$	an(-300^{\circ}) = \frac{\sin(-300^{\circ})}{\cos(-300^{\circ})} = \frac{-\frac{1}{2}}{\frac{\sqrt{3}}{2}} = -\frac{\sqrt{3}}{3}$$

Therefore, the best choice is (A).

Evaluate the Tangent of the Angle Without Using a Calculator −300∘- 300 ^ { \circ }−300∘

Evaluate the Tangent of the Angle Without Using a Calculator $- 300 ^ { \circ }$