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Homework Help: How to graph cosine and sine

  1. Oct 14, 2007 #1


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    I need help on graphing cosine and sine functions. i know how to read a graph and come up with the equation but i dont know how to do it the other way around. i want to be able to graph something like y=-2+2cos0.5x
  2. jcsd
  3. Oct 14, 2007 #2
  4. Oct 15, 2007 #3

    Gib Z

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    Homework Helper

    For any function in general, where [itex]y= a \cdot f( b (x-c) ) + d[/itex], to graph it we work from the inside out.

    So first graph f(x) as normal. Then move that graph c units to the right. If it is (x+c) instead, then c units to the left.

    Then squeeze the shifted graph by a factor of b times horizontally. If like in this case, its less than 1, write it in the form 1/b (b is 2 for your example). For when its in the form 1/b,
    then stretch it by a factor of b times horizontally.

    Then stretch the whole thing vertically by a factor of a. If a is negative, also flip the graph upside down. Similar thing, if a is less than one, rewrite the coefficient as 1/a. Then squeeze vertically by a factor of a.

    Now just must that up by d units, or if d is negative, down d units.

    Its really must easier to put into practice and to understand than it looks.

    For this one, get the normal Cosine graph, stretch it horizontally by a factor of 2. Eg where the normal cosine graph first intercepts the x axis at pi/2, it is now at pi.

    Then, stretch it up and down by a factor of 2. So all the points that it is 0 stay the same, where they are 1 they becoming 2, and where they were -1 they become -2.

    Now just shift that down by -2. So where they were -2, it becomes -4, and where they were 2, it becomes 0.

  5. Oct 15, 2007 #4


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    thanks i got
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