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Homework Help: Finding the domain and range without a calculator

  1. Sep 18, 2012 #1
    1. The problem statement, all variables and given/known data

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

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

    2. Relevant 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.

    3. 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.
  2. jcsd
  3. Sep 18, 2012 #2
    For what values of x, sec(x) is not defined?
  4. Sep 18, 2012 #3


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    Staff Emeritus
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    "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 [itex]\displaystyle y=\cos\left(\frac{\pi}{4}x\right)\ .[/itex]

    Where does this graph have zeros?

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