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Math Help - Pythagorean identities

  1. #1
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    Pythagorean identities

    Hi, I just learn about Pythagorean identities.
    As i know that cos^2θ + sin^2θ = 1
    but what is the work out to get 1? and why 1?

    Thanks.
    Last edited by lex3; April 28th 2010 at 07:04 AM.
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  2. #2
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    Quote Originally Posted by lex3 View Post
    Hi, I just learn about Pythagorean identities.
    As i know that cos^2θ + sin^2θ = 1
    but what is the work out to get 1? and why 1?

    Thanks.
    Consider a right triangle like here, i.e., the hypothenuse is denoted by h, opposite side is a and adjacent side is b.
    Then:
    sinθ=a/h
    cosθ=b/h
    and you know from Pythagorean theorem that a^2+b^2=h^2.
    So if you calculate cos^2\theta+\sin^2\theta, you get
    cos^2\theta+\sin^2\theta=\frac{a^2}{h^2}+\frac{b^2  }{h^2}=\frac{a^2+b^2}{h^2}=\frac{h^2}{h^2}=1.

    You can even simplify this by rescaling the triangle so that h=1. (In case you're familiar with unit circle definitions of trigonometric functions, you should know, what I mean.)

    BTW you have a whole article about this identity at wikipedia.
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  3. #3
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    Oh, now i understand.
    Thanks mate!
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