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Math Help - [SOLVED] Different Graphs of Sinx and Cosx

  1. #1
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    Cool [SOLVED] Different Graphs of Sinx and Cosx

    Hi, I know how to draw simple graphs like sinx, cosx, sin2x, cos2x ... etc.
    But I am stuck at the following:

    1) 2-2cos3x

    2) 3-4cos2x (for 0-180)

    3) 2-2cosx+2

    Could someone tell me the easiest way to draw these on a graph paper?

    I know that 3x or 2x in the above means the # of cycles in a 360 range. But I am confused about what to do when 3-4 or 1-2 is added in-front of the functions like in the above examples.
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  2. #2
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    Hello unstopabl3
    Quote Originally Posted by unstopabl3 View Post
    Hi, I know how to draw simple graphs like sinx, cosx, sin2x, cos2x ... etc.
    But I am stuck at the following:

    1) 2-2cos3x

    2) 3-4cos2x (for 0-180)

    3) 2-2cosx+2

    Could someone tell me the easiest way to draw these on a graph paper?

    I know that 3x or 2x in the above means the # of cycles in a 360 range. But I am confused about what to do when 3-4 or 1-2 is added in-front of the functions like in the above examples.
    OK. Here's how you do #1.

    First, when the graph of y= \cos3x is changed into y=2\cos3x, all the y-values are multiplied by 2. In other words, the graph is stretched up and down by a factor of 2, from the x-axis. Instead of taking values from -1 to 1, therefore, it will take values from -2 to +2.

    Next, when y = 2\cos3x is changed into y = -2\cos3x, all the y-values have their sign changed. In other words, the graph is reflected in the x-axis. So, for example, when x = 0,\; y = -2 instead of +2.

    Finally, changing y = -2\cos3x into y = 2-2\cos3x adds 2 to all the y-values. In other words, the graph is shifted (translated) upwards by 2 units.


    So:

    • Can you sketch the graph for #1 now?
      .
    • Can you do #2 in the same way?


    ***

    I assume that for #3 you mean
    y = 2-2\cos(x+2)
    Clearly, this is related to the graph of
    y = 2-2\cos x
    which you can sketch using the same techniques as above. Then, you need to learn that when x is changed into (x+2), the graph is translated 2 units to the left.

    Yes, it is to the left, not the right, because when x = 0, the value of (x+2) is 2. So the new graph starts at the point where x = 2 on the original graph. So it is exactly the same as the original, but it's 2 units to the left. (You may need to think a bit about that!)

    Can you complete #3 now?

    Grandad
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  3. #3
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    Makes perfect sense! Thanks for the detailed explanation, I have successfully drawn these graphs now

    There was a bit confusion in my post regarding #3

    The graph to be sketched was (2-2cosx)+2 so how would you draw this one?

    Would the +2 at the end just shift the whole graph 2 units upwards on the Y-Axis?
    Last edited by unstopabl3; May 7th 2010 at 05:39 AM.
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  4. #4
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    Hello unstopabl3
    Quote Originally Posted by unstopabl3 View Post
    Makes perfect sense! Thanks for the detailed explanation, I have successfully drawn these graphs now

    There was a bit confusion in my post regarding #3

    The graph to be sketched was (2-2cosx)+2 so how would you draw this one?

    Would the +2 at the end just shift the whole graph 2 units upwards on the Y-Axis?
    I'm not sure what you mean by (2-2\cos x)+2. This is just 4 - 2\cos x, isn't it?

    Grandad
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  5. #5
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    Haha yes it is, I feel embarrassed now, I think there was another question which I wanted to ask you and then just asked you the above idiotic one :d

    Thanks nonetheless, if I recall the one I need help with I'll let you know!

    Thanks again
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