the exact value of cos(17π/8) is: a. 0.99. b. √((2 + √2)/4). c. 0.38. d. √((2 - √2)/4).

Answer:

B. $\sqrt{\frac{2 + \sqrt{2}}{4}}$

Explanation:

Step1: Rewrite the angle

We know that $\frac{17\pi}{8}=2\pi+\frac{\pi}{8}$. Since $\cos(x + 2k\pi)=\cos(x)$ for any real - number $x$ and integer $k$, then $\cos\frac{17\pi}{8}=\cos\frac{\pi}{8}$.

Step2: Use the half - angle formula

The half - angle formula for cosine is $\cos\frac{\alpha}{2}=\pm\sqrt{\frac{1+\cos\alpha}{2}}$. Let $\alpha=\frac{\pi}{4}$, then $\frac{\alpha}{2}=\frac{\pi}{8}$. And $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$.

Step3: Substitute into the formula

$\cos\frac{\pi}{8}=\sqrt{\frac{1 + \cos\frac{\pi}{4}}{2}}=\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{2}}=\sqrt{\frac{2+\sqrt{2}}{4}}$.