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Math Help - Graphing csc and cot functions?

  1. #1
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    Graphing csc and cot functions?

    I am having trouble graphing these functions
    y=cot(1-pi/2)
    I know the period is pi
    the phase shift is pi/2
    But I cannot understand how to graph it

    the second function I am having trouble graphing is
    y=csc(2+pi)-3
    I know the period is pi
    the phase shift is -pi/2
    and the vertical shift is -3
    But I do not understand how to graph it either

    Can anyone help me graph these functions please?
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  2. #2
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    Quote Originally Posted by homeylova223 View Post
    I am having trouble graphing these functions
    y=cot(1-pi/2)


    y=csc(2+pi)-3
    Are these functions? Maybe you have left out a \theta or an x ?
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  3. #3
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    Yes I did not put the symbol you typed before x because I am not sure how to make that symbol with my keyboard that symbol you typed that look like an o I am not sure what it is called. That is the symbol that goes next to my 1 and 2 in the function sorry.
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    Quote Originally Posted by homeylova223 View Post
    Yes I did not put the symbol you typed before x because I am not sure how to make that symbol with my keyboard that symbol you typed that look like an o I am not sure what it is called. That is the symbol that goes next to my 1 and 2 in the function sorry.
    That symbol is called "theta" it has Greek origins, very popular in Mathematics when describing angles.

    So your functions are:

    \displaystyle y=\cot\left(\theta -\frac{\pi}{2}\right)

    \displaystyle y=\csc\left(2\theta +\pi\right)-3

    Do you know the general shape of these functions?

    Are you aware that

    \displaystyle y=\cot\left(\theta -\frac{\pi}{2}\right) =\frac{1}{\tan\left(\theta -\frac{\pi}{2}\right)}

    \displaystyle y=\csc\left(2\theta +\pi\right)-3=\frac{1}{\sin\left(2\theta +\pi\right)}-3
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    Ah I see the trouble I am having is that I am not sure how to use the phase shift on the cot function. I know the asymptotes of a regular cot function the only thing I am not sure is how to apply the phase shift. For example on the first one I know the phase shift is pi/2 and the period is pi. So would I start at pi/2 and end at 3pi/2 in order to complete the function? The thing is that the cot of pi/2 is zero then the cot of the next one 3pi/4 is negative 1 so I am kind of confused on how to make the phase shift.
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  6. #6
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    Quote Originally Posted by homeylova223 View Post
    The thing is that the cot of pi/2 is zero
    It is, but you take \frac{\pi}{2} within the function.

    \displaystyle \theta = \frac{\pi}{2} \implies y=\cot\left(\frac{\pi}{2} -\frac{\pi}{2}\right) =\frac{1}{\tan\left(\frac{\pi}{2} -\frac{\pi}{2}\right)}

    is now the asymptote.
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  7. #7
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    Oh I see so I have to plug in my values like pi/2 and 3pi/2 into the function. Then I graph these value ok.
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