Q.83 - Precalculus Enhanced with Graphing Utilities

Question

use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator: 

$\cos \left({400}^o\right)\sec \left({40}^o\right)$

Step-by-Step Solution

Answer

The exact value of $\cos \left({400}^o\right)\sec \left({40}^o\right)$ is $1$

Step 1: Given information

We are given a trigonometric function as $\cos \left({400}^o\right)\sec \left({40}^o\right)$

Step 2: use periodicity property of trigonometric function f ( θ + 2 π ) = f ( θ )

We get

$$\begin{gathered} \cos \left({400}^o\right)\sec \left({40}^o\right) \\ \cos \left({360}^o+{40}^o\right)\sec \left({40}^o\right) \\ \cos \left({40}^o\right)\sec \left({40}^o\right) \\ \cos \left({40}^o\right)\frac{1}{\cos \left({40}^o\right)} \\ =1 \end{gathered}$$

Step 3: Conclusion

The exact value of $\cos \left({400}^o\right)\sec \left({40}^o\right) is 1$.