Question

use reference angles to find the exact value of the following expression. do not use a calculator. tan 750°
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. tan 750° =
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize the denominator.)
b. the answer is undefined.

Explanation:

Step1: Find a coterminal angle

Subtract multiples of 360° from 750°. $750^{\circ}-2\times360^{\circ}=750^{\circ} - 720^{\circ}=30^{\circ}$.

Step2: Use the reference - angle property

The tangent function has a period of 180°, and $\tan\theta=\tan(\theta + 180^{\circ}n)$ for any integer $n$. Since 750° and 30° are coterminal, $\tan750^{\circ}=\tan30^{\circ}$.

Step3: Recall the value of $\tan30^{\circ}$

We know that $\tan30^{\circ}=\frac{\sin30^{\circ}}{\cos30^{\circ}}$, and $\sin30^{\circ}=\frac{1}{2}$, $\cos30^{\circ}=\frac{\sqrt{3}}{2}$. So $\tan30^{\circ}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$.

Answer:

A. $\tan750^{\circ}=\frac{\sqrt{3}}{3}$