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Math Help - equivalence relation trig. function

  1. #1
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    equivalence relation trig. function

    Please can somebody help.

    The \sim relation on  \Re is defined by x \simy if and only if  \sin ^2 x + \cos^2 y = 1 .
    Show that \sim is an equivalence relation on  \Re.

    Your help would be much appreciated.
    riptorn70.
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  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
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    Hi

    You need to show three things :
    • x\sim x
    • x\sim y \Leftrightarrow y\sim x (hint : use \sin^2t+\cos^2t=1)
    • (x \sim y \text{ and } y\sim z) \Rightarrow x\sim z (hint : sum the two relations \sin^2x+\cos^2y=1 and \sin^2y+\cos^2z=1)
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  3. #3
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    Thankyou flying squirrel that really helped.
    Riptorn70
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