ms sue! Algebra help

What are the graphs of y = cos x and y = sec x in the interval from -2pi to 2pi?

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  1. Please do not use my name as a school subject.

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    Ms. Sue
  2. You should be familiar with the cosine curve

    Look at the bottom of this page:
    http://www.regentsprep.org/regents/math/algtrig/att7/othergraphs.htm

    The cosine curve runs from -1 to +1.
    cos(0) = 1
    cos(60°) = 1/2
    cos(90) = 0
    cos(120) = -1/2
    etc
    since secx = 1/cosx
    at any given x , the secant is the reciprocal of the cosine value
    e.g. cos(60) = 1/2, thus sec(60) = 2
    which means that when the cosine value is zero, (as it crosses the x-axis) , we would have the reciprocal of zero , which of course is undefined
    So we have vertical asymptotes whenever the cosine value is 0.
    The result is a series of U shaped curves sitting on top or falling below the cosine curve as you can seen in the graph I gave you

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  3. yes. that is right. and good morning mrs. sue

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