# Thread: The domain and range of a secant function

1. ## The domain and range of a secant function

After over an hour of pondering, I cannot seem to be able to figure out how to do this problem. I have taken pre-calculus and trigonometry and am in calculus 1 right now where we are "reviewing." Anyways, here is the problem, I was just looking for some help on how to solve it.

(The solution guide steps are right under it but I can't seem to figure out what's going on.)

Find the domain and range.

Thanks by the way.

2. Originally Posted by JustinParker
After over an hour of pondering, I cannot seem to be able to figure out how to do this problem. I have taken pre-calculus and trigonometry and am in calculus 1 right now where we are "reviewing." Anyways, here is the problem, I was just looking for some help on how to solve it.

(The solution guide steps are right under it but I can't seem to figure out what's going on.)

Find the domain and range.

Thanks by the way.

Remember

$\displaystyle\sec{x}=\frac{1}{\cos{x}}$

The denominator can't be 0.

3. Originally Posted by dwsmith
Remember

$\displaystyle\sec{x}=\frac{1}{\cos{x}}$

The denominator can't be 0.
Well, I am aware of both of those things. But if they pertain to the problem I can't seem to see the connection. Thanks though.

4. Originally Posted by JustinParker
Well, I am aware of both of those things. But if they pertain to the problem I can't seem to see the connection. Thanks though.
$\displaystyle\sec{\left(\frac{t\pi}{4}\right)}=\fr ac{1}{\cos{\left(\frac{t\pi}{4}\right)}}$

$\displaystyle\cos{x}=0 \ \mbox{when} \ \ x=\frac{\pi}{2}+\pi k \ \ k\in\mathbb{Z}$

What value of t makes $\displaystyle\frac{t\pi}{4}=\frac{\pi}{2}+\pi k\mbox{?}$

$t=...,-2,2,6,10,...$

How do you represent those integers?

5. Originally Posted by JustinParker
Well, I am aware of both of those things. But if they pertain to the problem I can't seem to see the connection. Thanks though.
Then I guess the question is "are you clear on what 'domain' means here?" Do you see why values of x such that cos(x)= 0 and so the denominator in $sec(x)= \frac{1}{cos(x)}$ is 0 are NOT in the domain?

As far as the range is concerned, $-1\le cos(x)\le 1$ so what can you say about $sec(x)= \frac{1}{cos(x)}$?

6. Ok thanks. Between dwsmith's domain help and hallsofivy's range help I believe I understand everything here. Thanks so much.

7. It would be good too if you tried to answer the questions asked to you to see if you grasped what they tried to make you understand

8. might help to see how the graphs of y = cos(x) and y = sec(x) are related ...

,

,

,

,

,

,

,

# how to find the range of a secant function

Click on a term to search for related topics.