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Math Help - Trig graphs

  1. #1
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    Jul 2008
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    Trig graphs

    Hello!
    Hope someone can help with a bit of confusion i have!?

    Im happy with sketching trig graphs generally but this question caught me out and i cant get my head around it!!....

    "Sketch the graph of y = 1 + 3cosec2x". I thought that was simply the graph of y = cosec x stretched with scale factor 1/2 and 3 in the x and y direction respectively followed by a translation of vector (0, 1). This is where i went wrong, i drew my graph with the translation of 1 unit in the y direction when actually the stretch in the y direction had moved the vertexes of the upper parbolas a further 3 units up.

    Why does a stretch in the y direction on this graph expand the series of parbolas away for the x axis thus moving the vertexes when the same transformation when applied to a single parbola ie y = 3(-x^2) does not move the location of the vertex?

    Hope that makes sense!

    Thanks for any help in advance.
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  2. #2
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    Jul 2008
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    If the function that the coefficient multiplies is anything other than zero, it will move away from the x axis. The vertex in x^2 is the same as 3(x^2) because 3 times 0 = 0. CSC pi/2 = 1. 3*1 = 3
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  3. #3
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    Jul 2008
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    Hello,
    Thanks a lot, just had an experiment on my calculator! seems a bit clearer now but we shall see!
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