Question

Use the even–odd properties to find the exact value of each expression. Do not use a calculator.

$\sec (-\mathrm{\pi })$

Short answer

The exact value of trigonometry expression is -1.

Step-by-step solution

Step 1. Given Information

Given that the trigonometry expression is $\sec (-\mathrm{\pi }).$To find the exact value of trigonometry expression using even odd function.

Step 2. Even odd property

Secant is an even function and it can be denoted as,

$$\begin{gathered} \sec (-\mathrm{\theta })=-\mathrm{sec\theta } \\ =\frac{1}{\mathrm{cos\theta }} \\ =\frac{1}{\mathrm{x}} \end{gathered}$$

The point on the circle corresponds to the given angle can be substituted.

$$\begin{gathered} \sec (-\mathrm{\pi })=-\mathrm{sec\pi } \\ =\frac{1}{\mathrm{cos\pi }} \\ =\frac{1}{-1} \\ \sec (-\mathrm{\pi })=-1 \end{gathered}$$