# Finding the domain and range without a calculator

## Homework Statement

Find the domain and range of the following function without the use of a calculator:

f(x) = sec (pi x/4)

## Homework Equations

As far as I know, this problem doesn't specifically require "equations". Therefore I am leaving this section blank. Not because I am a malicious poster that is trying to break the rules and upset the administration here, but simply because I don't know any equations for this problem.

## The Attempt at a Solution

I tried flipping this and finding the cosine of 4pi and graphing it. But I failed to come up with a valid graph and was puzzled. I could take a picture of my "graph", but I don't think anyone could read it. Help would be greatly appreciated here.

For what values of x, sec(x) is not defined?

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

Find the domain and range of the following function without the use of a calculator:

f(x) = sec (pi x/4)

## Homework Equations

As far as I know, this problem doesn't specifically require "equations". Therefore I am leaving this section blank. Not because I am a malicious poster that is trying to break the rules and upset the administration here, but simply because I don't know any equations for this problem.

## The Attempt at a Solution

I tried flipping this and finding the cosine of 4pi and graphing it. But I failed to come up with a valid graph and was puzzled. I could take a picture of my "graph", but I don't think anyone could read it. Help would be greatly appreciated here.
"I tried flipping this and finding the cosine of 4pi ..."

That won't work.

sec(θ) = 1/(cos(θ)). It's not equal to cos(1/θ), nor 1/(cos(1/θ)).

Consider the graph of $\displaystyle y=\cos\left(\frac{\pi}{4}x\right)\ .$

Where does this graph have zeros?

What are the maximum & minimum values for y on this graph?