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Math Help - [SOLVED] What is the identity used here?

  1. #1
    Member sinewave85's Avatar
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    [SOLVED] What is the identity used here?

    This is part of a larger example problem that I came across in reviewing. I can't for the life of me remember the identity or principle that would get one from the first form to the second in one step. Maybe it is not one step -- the authors of the textbook eliminated what they assumed one would see automatically? I realize this may be a stupid question, but it is driving me crazy. Anyone?

    \cos{(\pi-2\theta)} = \frac{20-x}{x}

    \cos{(2\theta)} = \frac{x-20}{x}
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  2. #2
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    Hello sinewave85
    Quote Originally Posted by sinewave85 View Post
    This is part of a larger example problem that I came across in reviewing. I can't for the life of me remember the identity or principle that would get one from the first form to the second in one step. Maybe it is not one step -- the authors of the textbook eliminated what they assumed one would see automatically? I realize this may be a stupid question, but it is driving me crazy. Anyone?

    \cos{(\pi-2\theta)} = \frac{20-x}{x}

    \cos{(2\theta)} = \frac{x-20}{x}
    For any angle \theta, \cos(\pi-\theta) =-\cos(\theta)

    So \cos(\pi-2\theta) = \frac{20-x}{x}

    \Rightarrow -\cos(2\theta) = \frac{20-x}{x}

    \Rightarrow\cos(2\theta) = -\frac{20-x}{x} = \frac{x-20}{x}

    Grandad
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  3. #3
    Member sinewave85's Avatar
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    Quote Originally Posted by Grandad View Post

    For any angle \theta, \cos(\pi-\theta) =-\cos(\theta)
    Thanks, Grandad! I knew it had to be something simple (kind of embarased that it was that basic), but unfortunately those are sometimes the hardest things for me to remember. You saved me a lot of searching and headbanging.

    P.S. And thanks for writing out all of the steps so nicely! It helps to see each little adjustment.
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