Q. 26 - Precalculus Enhanced with Graphing Utilities

Question

In problems 11-26, use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.

$\sec \left(\frac{25\pi }{6}\right)$

Step-by-Step Solution

Answer

The exact value is $\frac{2\sqrt{3}}{3}$.

Step 1. Given information.

We have:

$\sec \left(\frac{25\pi }{6}\right)$

Step 2. Find the exact value of trigonometric function.

The function is $\sec \left(\frac{25\pi }{6}\right)$.

$\sec \left(\frac{25\pi }{6}\right)=\frac{1}{\cos \left(\frac{25\pi }{6}\right)}$

Formula used:

$\cos \left(2\pi +\theta \right)=\cos \left(\theta \right)$

$$\begin{gathered} =\frac{1}{\cos \left(\frac{\pi }{6}\right)} \\ =\frac{1}{\frac{\sqrt{3}}{2}} \\ =\frac{2\sqrt{3}}{3} \end{gathered}$$