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Math Help - Finding trig identity on calculator?

  1. #1
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    Finding trig identity on calculator?

    EDIT: I actually went back and re watched the video a few times and realized that he disengaged the bottom two functions. I'm sorry if this took up anyone's time. Can anyone tell me how to graph functions simultaneously on a graphing calculator?

    Hi. I'm following along on a precalculus video from my professor. In the very first problem, he graphs a trigonometric equation in the calculator to see if it is an identity. I'm not getting the same graph as he is, and I'm not sure what's wrong. I have it on zoom trig but my graph is different than his.

    This is the problem:

    Is cos2x = 2(cosx^2)-1 an identity?

    Here is the video. It's the very first problem he covers.



    Thanks in advance. Please let me know if you need more information.
    Last edited by FatimaA; June 12th 2013 at 05:43 PM.
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  2. #2
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    Re: Finding trig identity on calculator?

    \displaystyle \begin{align*} \cos{(2x)} = 2\cos^2{(x)} - 1 \end{align*} is an identity.

    Here's a nice proof of the angle sum identity for cosine: \displaystyle \begin{align*} \cos{ \left(\alpha + \beta \right) } = \cos{(\alpha )}\cos{(\beta )} - \sin{(\alpha )}\sin{(\beta)}  \end{align*}

    And in the case where \displaystyle \begin{align*} \alpha = \beta = x \end{align*} then that gives

    \displaystyle \begin{align*} \cos{ \left( x + x \right) } &= \cos{(x)}\cos{(x)} - \sin{(x)}\sin{(x)} \\ \cos{(2x)} &= \cos^2{(x)} - \sin^2{(x)} \\ &= \cos^2{(x)} - \left[ 1 - \cos^2{(x)} \right] \textrm{ by the Pythagorean Identity} \\ &= \cos^2{(x)} - 1 + \cos^2{(x)} \\ &= 2\cos^2{(x)} - 1 \end{align*}

    Q.E.D.
    Thanks from FatimaA
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