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trig

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I need to state the period and 2 consecutive asymptotes on the graph for the following questions.

1: y = -3 tan pi*x
period: pi (?)
asymptotes: ?

2: y = 2 sec 4x
period: ?
asymptotes: ?

3: y = csc (x/3)
period: ?
asymptotes: ?

4: y = 3 cot (pi*x/2)
period: ?
asymptotes: ?


If possible, I'd love some explanation/clarification for the answers as well so I can understand it better... thanks!

  • trig -

    1: y = -3 tan pi*x
    period: pi (?)
    asymptotes: ?
    ------------------------
    Well, I will help with the first one. Then you better try to use a similar approach on the rest
    y = -3 sin pi x/ cos pi x
    this repeats when pi x = pi
    or period = 1 pi
    It gets undefined when cos pi x = 0
    or pi x = pi/2 which is x = 1/2
    then pi x = 3 pi/2 which is x = 3/2

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