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Math Help - Principle behind compressing trig functions

  1. #1
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    Principle behind compressing trig functions

    Hi!

    What's the idea behind compressing functions when graphing, compressing horizontally or vertically:

    1. y = \sec 2x\ \text{versus}\ 2 \sec x

    There is no amplitude, what's the function of the second 2?

    2. y = \sec \frac12x\ \text{versus}\ \frac12 \sec x
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Principle behind compressing trig functions

    Consider the function y_1 = f(x) -- if the constant A is introduced then the function y_1=Af(x) will be stretched vertically by factor A, and the function y_3=f(Ax) will be squeezed horizontally by factor A. Here is an example where y_1 = sin(x) and A = 3. See how y_2 = 3sin(x) is streteched vertically while its period remains the same, and y_3 = sin(3x) is squeezed horizontally while it's height remains the same?
    Attached Thumbnails Attached Thumbnails Principle behind compressing trig functions-sine.jpg  
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