Question

use reference angles to find the exact value of the following expression. tan 330°. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. tan 330° = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expressio) b. the answer is undefined.

Explanation:

Step1: Find the reference angle

The angle $330^{\circ}$ is in the fourth - quadrant. The reference angle $\theta_{r}$ for an angle $\theta = 330^{\circ}$ is $360^{\circ}-330^{\circ}=30^{\circ}$.

Step2: Determine the sign of the tangent function

In the fourth - quadrant, the tangent function is negative. That is, $\tan\theta<0$ when $\theta$ is in the fourth - quadrant.

Step3: Use the value of the tangent of the reference angle

We know that $\tan30^{\circ}=\frac{\sqrt{3}}{3}$. Since $\tan330^{\circ}=-\tan30^{\circ}$ (because of the sign in the fourth - quadrant), then $\tan330^{\circ}=-\frac{\sqrt{3}}{3}$.

Answer:

A. $\tan330^{\circ}=-\frac{\sqrt{3}}{3}$