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Math Help - Graphing trig expressions such as sin(1/x)

  1. #1
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    Graphing trig expressions such as sin(1/x)

    Hello,

    How would I go about sketching for example the graph of sin(1/x) (without using software). What though process should I go through? I am thinking about drawing the graph of sin(x) and trying to think about what happens when x increases?

    Many thanks for any help,
    Aaron.
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  2. #2
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    Not bad, but you must pay careful attention.

    1) y = sin(x) is wonderfully periodic and you will not ever find anything interesting, unless
    2) You figure out that your transformation x ==> 1/x is NOT linear.
    2a) [1,10] ==> [1,0.1]
    2b) [10,100] ==> [0.1,0.01]
    2c) [100,1000] ==> [0.01,0.001]

    For 2a, we mapped 9 greater than 1 onto 0.9 less than 1. That's quite a bit of compression.
    For 2b, we mapped 90 greater than 10 onto 0.09 less than 0.1. That's a whole bunch of compression.
    For 2c, ... are you seeing it, yet?
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  3. #3
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    Ok, I can see that because the 1/x part is not linear, as it gets closer to x = 0 (which is not defined) it compresses until it gets to that undefined value. How would I determine what the graph looks like when the x values get large? I suppose 1/x gets very small, does the curve continue oscillating or does it converge?
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