Question

In problems 11-26,use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.

$\sec \left({420}^{\circ \hspace{0.17em}}\right)$

Short answer

The exact value is$2$.

Step-by-step solution

Step 1. Given information.     

We have:

$\sec \left({420}^{\circ \hspace{0.17em}}\right)$

Step 2. Find the exact value of trigonometric function.      

The function is $\sec \left({420}^{\circ \hspace{0.17em}}\right)$.

Formula used:

$sec\left(\theta +2\pi \right)=sec\theta$

Here, $\theta =60°$

It follows:

$$\begin{gathered} sec\left(60°+360°\right)=sec60° \\ =\frac{1}{\cos \left({60}^{\circ \hspace{0.17em}}\right)} \\ =\frac{1}{\frac{1}{2}} \\ =2 \end{gathered}$$