Q 135 - Precalculus Enhanced with Graphing Utilities

Question

Explain how to find the value of $\cos (-{45}^o)$ using even–odd

properties.

Step-by-Step Solution

Answer

The value of $\cos \left(-{45}^o\right)$ is :-

$\frac{1}{\sqrt{2}}$

Step 1. Given Information

We have to find the value of $\cos \left(-{45}^o\right)$.

We will use odd-even properties of cosine function to find the value of  $\cos \left(-{45}^o\right)$.

Step 2. To find the value

We have to find the value of $\cos (-{45}^o)$.

We know that cosine function is an even function. 

That is :-

$\cos (-\theta )=\cos \theta$.

By using this property of cosine function we have :- 

$\cos (-{45}^o)=\cos {45}^o$.

We know that the value of $\cos {45}^o=\frac{1}{\sqrt{2}}$.

By putting this value, we have :- 

$\cos (-{45}^o)=\frac{1}{\sqrt{2}}$.