Question

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

$\cos (-\frac{\mathrm{\pi }}{4})$

Short answer

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

Step-by-step solution

Step 1. Given information

Given that the trigonometric expression is $\cos (-\frac{\mathrm{\pi }}{4}).$To find the value of trigonometric expression using even odd property.

Step 2. Even odd property

On using even odd property,

$$\begin{gathered} \cos (-\mathrm{\theta })=-\mathrm{cos\theta } \\ \cos (-\frac{\mathrm{\pi }}{4})=\cos \frac{\mathrm{\pi }}{4} \\ \cos \frac{\mathrm{\pi }}{4}=\frac{\sqrt{2}}{2} \\ \cos (-\frac{\mathrm{\pi }}{4})=\frac{\sqrt{2}}{2} \end{gathered}$$