Use the Half-angle Formulas to find the exact value of the trigonometric function.
-$\tan 165 ^ { \circ }$
A) $- 2 - \sqrt { 3 }$
B) $- 2 + \sqrt { 3 }$
C) $2 - \sqrt { 3 }$
D) $2 + \sqrt { 3 }$

Question

Quizplus · Accepted Answer

To find $\tan 165^\circ$, we can use the half-angle formula for tangent: $\tan \left(\frac{\theta}{2}\right) = \sqrt{\frac{1 - \cos \theta}{1 + \cos \theta}}$. Since $165^\circ = 330^\circ / 2$, we find $\cos 330^\circ = \sqrt{3}/2$. Plugging this into the formula gives $\tan 165^\circ = \sqrt{\frac{1 - \sqrt{3}/2}{1 + \sqrt{3}/2}} = -2 + \sqrt{3}$.

Use the Half-Angle Formulas to Find the Exact Value of the Trigonometric