Question

use reference angles to find the exact value. rationalize the denominator of your answer, if needed. select \undefined\ if applicable. sec(17π/4) = □

Explanation:

Step1: Rewrite secant as 1/cosine

$\sec x=\frac{1}{\cos x}$, so $\sec\frac{17\pi}{4}=\frac{1}{\cos\frac{17\pi}{4}}$.

Step2: Reduce the angle

Subtract full - circles ( $2\pi$) from $\frac{17\pi}{4}$. $\frac{17\pi}{4}-4\pi=\frac{17\pi - 16\pi}{4}=\frac{\pi}{4}$. So $\cos\frac{17\pi}{4}=\cos\frac{\pi}{4}$.

Step3: Find cosine value

We know that $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$.

Step4: Calculate secant value

$\sec\frac{17\pi}{4}=\frac{1}{\cos\frac{17\pi}{4}}=\frac{1}{\cos\frac{\pi}{4}}=\frac{1}{\frac{\sqrt{2}}{2}}=\sqrt{2}$.

Answer:

$\sqrt{2}$