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Math Help - The domain and range of a secant function

  1. #1
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    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.
    The domain and range of a secant function-math-problem.jpg


    Thanks by the way.
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  2. #2
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    Quote Originally Posted by JustinParker View Post
    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.
    Click image for larger version. 

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ID:	20438


    Thanks by the way.

    Remember

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

    The denominator can't be 0.
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    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.
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  4. #4
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    Quote Originally Posted by JustinParker View Post
    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?
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  5. #5
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    Quote Originally Posted by JustinParker View Post
    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)}?
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  6. #6
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    Ok thanks. Between dwsmith's domain help and hallsofivy's range help I believe I understand everything here. Thanks so much.
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  7. #7
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    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
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  8. #8
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    might help to see how the graphs of y = cos(x) and y = sec(x) are related ...
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