Question

use a graphing calculator to evaluate. round to 3 decimal places.
sec(\frac{2}{9}\pi)=\square
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question 13

Explanation:

Step1: Recall the reciprocal identity

$\sec x=\frac{1}{\cos x}$. So, $\sec(\frac{2}{9}\pi)=\frac{1}{\cos(\frac{2}{9}\pi)}$.

Step2: Calculate the value of $\cos(\frac{2}{9}\pi)$

Using a graphing calculator, $\cos(\frac{2\pi}{9})\approx0.766$.

Step3: Calculate the value of $\sec(\frac{2\pi}{9})$

Since $\sec(\frac{2\pi}{9})=\frac{1}{\cos(\frac{2\pi}{9})}$, then $\sec(\frac{2\pi}{9})=\frac{1}{0.766}\approx1.305$.

Answer:

$1.305$