Q. 46 - Precalculus Enhanced with Graphing Utilities

Question

What is the domain and the range of the secant function? What is the period?

Step-by-Step Solution

Answer

The range is $sec\theta \ge 1,sec\theta \le 1$

Step 1: Given information

Given the secant function

Step 2: Checking the points where the function is not defined

Here

$sec\theta =\frac{1}{\cos \theta }$

Cosine is not defined at odd integer multiples of $\frac{\mathrm{\pi }}{2}$

The range of cosine is $-1\le x\le 1$

So the range is $sec\theta \le 1,sec\theta \ge 1$