Chapter 12.1, Problem 64E

To determine

To graph: The trigonometric function $y=\sec 2\theta -3$ .

Explanation of Solution

Given information:

The trigonometric function $y=\sec 2\theta -3$ .

Graph:

Consider the trigonometric function $y=\sec 2\theta -3$ .

Construct a table of values for different $\theta$ .

  $\begin{array}{cc}\theta & y=\sec 2\theta -3\\ 0& -2\\ \frac{\pi }{6}& -1\\ \frac{\pi }{4}& -\\ \frac{\pi }{3}& -5\\ \frac{\pi }{2}& -4\end{array}$

Sketch the function in two dimensional plane.

  

Interpretation:

The function $y=\sec 2\theta -3$ has period $\pi$ , the domain of the function is $ℝ-\frac{\pi }{2}n$ where n is odd integer. The x-intercept does not exists. The y-intercept is 1. The asymptotes of the function are $x=\frac{\pi }{2}n$ where n is odd.