Question

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

$\sec (-\frac{\mathrm{\pi }}{6})$

Short answer

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

Step-by-step solution

Step 1. Given information

Given that the trigonometry expression is $\sec (-\frac{\mathrm{\pi }}{6}).$To find the exact value of expression using even odd property.

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 can be substituted on the unit circle responds to the given angle.

$$\begin{gathered} \sec (-\frac{\mathrm{\pi }}{6})=-\sec \frac{\mathrm{\pi }}{6} \\ =\frac{1}{\mathrm{cos\pi }} \\ =\frac{1}{{\displaystyle \frac{\sqrt{3}}{2}}} \\ \sec (-\frac{\mathrm{\pi }}{6})=\frac{2\sqrt{3}}{3} \end{gathered}$$