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Math Help - Complementary Angle Theorem

  1. #1
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    Complementary Angle Theorem

    There is an effect of the complementary angle theorom that I don't understand. For example:

    sin squared(40) + sin squared(50) = sin squared(40) + cos squared(40) = 1

    This previous statement's purpose was to show how sin(50) = cos(40), but what got me was the answer being equal to 1. Doing some experimenting, to see if this is a rule:

    sin squared(10) + sin squared(80) = sin squared(10) + cos squared(10) = 1

    and so on:

    cos squared(10) + cos squared(80) = 1
    sin squared(30) + sin squared(60) = 1

    Why is it, when these functions are squared, that the answer = 1?
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  2. #2
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    Quote Originally Posted by spiritualfields
    There is an effect of the complementary angle theorom that I don't understand. For example:

    sin squared(40) + sin squared(50) = sin squared(40) + cos squared(40) = 1

    This previous statement's purpose was to show how sin(50) = cos(40), but what got me was the answer being equal to 1. Doing some experimenting, to see if this is a rule:

    sin squared(10) + sin squared(80) = sin squared(10) + cos squared(10) = 1

    and so on:

    cos squared(10) + cos squared(80) = 1
    sin squared(30) + sin squared(60) = 1

    Why is it, when these functions are squared, that the answer = 1?
    Pythagoras' theorem in terms of trig functions is:

    <br />
\sin^2(x)+\cos^2(x)=1<br />

    RonL
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  3. #3
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    Okay, I see it now. Thanks.
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  4. #4
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    Quote Originally Posted by spiritualfields
    There is an effect of the complementary angle theorom that I don't understand. For example:

    sin squared(40) + sin squared(50) = sin squared(40) + cos squared(40) = 1
    ...
    Hello,

    I've attached a diagram to show you what I've calculated.

    If the sum of the 2 angles is 90 you are dealing with a right triangle.

    \alpha+\beta=90^\circ \Longrightarrow \beta=90^\circ-\alpha

    The red line corresponds to \sin(\alpha) and the blue line corrsponds to \sin(\beta)=sin(90^\circ-\alpha)

    According to the diagram is: (\mbox{red})^2+(\mbox{blue})^2=1

    Plug in the sine values and you'll get the property you have detected.

    The blue line corresponds to \cos(\alpha). So now you can easily complete the Pythagoran rule of the Sine and Cosine function.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Complementary Angle Theorem-pyth_theorem1.gif  
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  5. #5
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    spiritualfields

    earboth, thanks. What program did you use to draw that?
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  6. #6
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    Quote Originally Posted by spiritualfields
    earboth, thanks. What program did you use to draw that?
    Hello,

    have a look here: http://www.dynageo.de

    Greetings

    EB
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