Q. 13 - Precalculus Enhanced with Graphing Utilities

Question

Find the exact value of the expression. Do not use a calculator.

$\frac{\cos \left(-{40}^{°}\right)}{\cos {40}^{°}}$

Step-by-Step Solution

Answer

The exact value of the expression $\frac{\cos \left(-{40}^{°}\right)}{\cos {40}^{°}}$ is,1.

Step 1 Given expression is,

$\frac{\cos \left(-{40}^{°}\right)}{\cos {40}^{°}}$.

The objective is, we need to find the exact value for the given expression.

Step 2 we know that,

$$\begin{gathered} \cos \left(-\theta \right)=\cos \theta \\ \cos \left(-{40}^{°}\right)=\cos {40}^{°} \end{gathered}$$

So, the given expression becomes,

$$\begin{gathered} \frac{\cos \left(-{40}^{°}\right)}{\cos {40}^{°}}=\frac{\cos {40}^{°}}{\cos {40}^{°}} \\ =1 \end{gathered}$$