Question

use the unit circle to find the value of cos(π/4) and periodic properties of trigonometric functions to find the value of cos(17π/4). answer boxes in your choice. a. cos(π/4) = √2/2 (type an exact answer, using radicals as needed. simplify your answer. rationalize the denominator.) b. the solution is undefined. select the correct choice below and fill in any answer boxes in your choice. a. cos(17π/4) = (type an exact answer, using radicals as needed. simplify your answer. rationalize the denominator.) b. the solution is undefined.

Explanation:

Step1: Recall unit - circle values

On the unit circle, for the angle $\theta=\frac{\pi}{4}$, the coordinates of the corresponding point are $(\cos\frac{\pi}{4},\sin\frac{\pi}{4})=(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$. So, $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$.

Step2: Use periodicity of cosine function

The cosine function $y = \cos x$ has a period of $2\pi$. We can write $\frac{17\pi}{4}=4\pi+\frac{\pi}{4}$. Since $\cos(x + 2k\pi)=\cos x$ for any real - number $x$ and integer $k$, when $x=\frac{\pi}{4}$ and $k = 2$, we have $\cos\frac{17\pi}{4}=\cos(4\pi+\frac{\pi}{4})=\cos\frac{\pi}{4}$.

Answer:

A. $\cos\frac{17\pi}{4}=\frac{\sqrt{2}}{2}$