Chapter 6, Problem 85RE

To determine

To FIND: Domain, Range and Period of secant function

Answer to Problem 85RE

Domain of secant function

$\theta :\left(-\infty ,\infty \right)$ except $\theta :n\pi$

Where n is any integer

Range: $y:\left(-1,-\infty \right)\cup \left(1,\infty \right)$

Explanation of Solution

Given information:

The secant functions

Formula used:

Domain is the set of input values for function

Range is set of output for function

Graph of $y=\sec \theta$

As we know, $\sec x=\frac{1}{\cos x}$

So, the domain of secant function is

$\theta :\left(-\infty ,\infty \right)$ except $\theta :n\pi$

Where n is any integer

Range: As we can see in graph $y=\sec x$ ,

y differs from $\left(-\infty ,-1\right)\cup \left(1,\infty \right)$ ,

Range: $y:\left(-\infty ,-1\right)\cup \left(1,\infty \right)$