Question

use the unit circle to find the value of tan π and even or odd trigonometric functions to find the value of tan (-π). select the correct choice below and fill in any answer boxes within your choice. a. tan π = 0 (type an exact answer, using radicals as needed. simplify your answer. rationalize the denominator.) b. the expression is undefined. select the correct choice below and fill in any answer boxes within your choice. a. tan (-π) = (type an exact answer, using radicals as needed. simplify your answer. rationalize the denominator.) b. the expression is undefined.

Explanation:

Step1: Recall tangent formula

The formula for $\tan\theta=\frac{\sin\theta}{\cos\theta}$.

Step2: Find $\sin\pi$ and $\cos\pi$ on unit - circle

On the unit - circle, for $\theta = \pi$, the coordinates of the corresponding point are $(-1,0)$. Since $\sin\theta$ is the $y$ - coordinate and $\cos\theta$ is the $x$ - coordinate, we have $\sin\pi = 0$ and $\cos\pi=-1$.

Step3: Calculate $\tan\pi$

$\tan\pi=\frac{\sin\pi}{\cos\pi}=\frac{0}{-1}=0$.

Step4: Recall the property of tangent function

The tangent function is an odd function, i.e., $\tan(-\theta)=-\tan\theta$.

Step5: Calculate $\tan(-\pi)$

Since $\tan\pi = 0$, then $\tan(-\pi)=-\tan\pi=- 0 = 0$.

Answer:

A. $\tan\pi = 0$
A. $\tan(-\pi)=0$