Question

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

Explanation:

Step1: Recall cosine - unit circle relationship

On the unit circle, for an angle $\theta$, $\cos\theta$ is the $x$ - coordinate of the point where the terminal side of the angle intersects the unit circle.

Step2: Locate angle $\pi$ on unit - circle

The angle $\theta=\pi$ radians corresponds to the point $(- 1,0)$ on the unit circle.

Step3: Determine $\cos\pi$

Since $\cos\theta$ is the $x$ - coordinate of the point on the unit circle corresponding to the angle $\theta$, for $\theta = \pi$, $\cos\pi=-1$.

Step4: Recall property of cosine function

The cosine function is an even function, i.e., $\cos(-\theta)=\cos\theta$. So, $\cos(-\pi)=\cos\pi=-1$.

Answer:

A. $\cos\pi=-1$