Question

use reference angles to find the exact value of the following expression. tan(-\frac{\pi}{4}) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. tan(-\frac{\pi}{4}) = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbe b. the answer is undefined.

Explanation:

Step1: Determine the reference angle

The angle $\theta =-\frac{\pi}{4}$ is in the fourth - quadrant. The reference angle $\theta_{r}$ for an angle $\theta$ in the fourth - quadrant is given by $\theta_{r}=|\theta|$. So, for $\theta =-\frac{\pi}{4}$, the reference angle $\theta_{r}=\frac{\pi}{4}$.

Step2: Recall the tangent function properties

The tangent function has the property $\tan(-\alpha)=-\tan(\alpha)$. Also, $\tan(\frac{\pi}{4}) = 1$. So, $\tan(-\frac{\pi}{4})=-\tan(\frac{\pi}{4})$.

Step3: Calculate the value

Since $\tan(\frac{\pi}{4}) = 1$, then $\tan(-\frac{\pi}{4})=- 1$.

Answer:

A. $\tan(-\frac{\pi}{4})=-1$