Chapter 6.7, Problem 35E

To determine

To find: the value of $\theta$ where the two graphs are tangent to each other.

Answer to Problem 35E

They are related inversely by definition.

Explanation of Solution

Given information:

  $\begin{array}{l}y=\cos \theta \\ y=\sec \theta \\ \text{Interval: }-2\pi \text{ and }2\pi \end{array}$

Calculation:

Let $x=\theta$ . Substitute different $x$ values for the given intervals into the given equation to acquire $y$ values. Please note if you acquire any undefined $y$ values, then you have found your asymptote. Then pair up the respective $x$ and $y$ values to form coordinate points. Plot the coordinate points and connect the points to create the graphed function as shown below.

Notice the relationship between the two graphs. The parts where the secant is missing the cosine graph makes up for it. This is because these two functions are related inversely the graph seen above is the result.