Question

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

$\sec (-{60}^{\mathrm{o}})$

Short answer

The exact value of trigonometric expression is 2.

Step-by-step solution

Step 1. Given Information

Given that the trigonometric function is $\sec (-{60}^{\mathrm{o}}).$To find the exact value of trigonometric function using even odd property.

Step 2. Even odd property

Secant is an even function can be denoted as,

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

The value can be substituted in the given function.

$$\begin{gathered} \sec (-{60}^{\mathrm{o}})=\sec \left({60}^{\mathrm{o}}\right) \\ =\frac{1}{\mathrm{x}} \\ =\frac{1}{{\displaystyle \frac{1}{2}}} \\ \sec (-{60}^{\mathrm{o}})=2 \end{gathered}$$