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Math Help - GRAPH OF COSine FUNCTION

  1. #1
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    GRAPH OF COSine FUNCTION

    sketch the graph of cosine for 0<\theta<2\pi

    y=2-\mid cos\frac{\theta}{2}\mid
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  2. #2
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    Note that 2-\bigg|\cos\left(\dfrac{\theta}{2}\right)\bigg| = 2-\sqrt{\cos^2\left(\dfrac{\theta}{2}\right)}
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  3. #3
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    Quote Originally Posted by mastermin346 View Post
    sketch the graph of cosine for 0<\theta<2\pi

    y=2-\mid cos\frac{\theta}{2}\mid
    hi

    first off , do you know how to sketch the graph of cos 1/2 Θ ?

    Note that its period is 2π/(1/2)=4π

    The usual graph we draw (cos Θ) has a period of 2π but this time , 4π .

    |cos 1/2 Θ| - reflect the negative part of the graph to the postive side

    - |cos 1/2 Θ| - reflect the whole graph about the x-axis

    2 - |cos 1/2 Θ| - shift the graph up by 2 units .
    Attached Thumbnails Attached Thumbnails GRAPH OF COSine FUNCTION-trigo-functin.jpg  
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  4. #4
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    Quote Originally Posted by mastermin346 View Post
    sketch the graph of cosine for 0<\theta<2\pi

    y=2-\mid cos\frac{\theta}{2}\mid
    cos(0)=1

    cos\left(\frac{{\pi}}{2}\right)=0

    cos\left(\frac{\theta}{2}\right)=0\ \Rightarrow\ \frac{\theta}{2}=\frac{{\pi}}{2}\ \Rightarrow\ \theta={\pi}

    cos\left(\frac{\theta}{2}\right) has twice the period that cos\theta has

    or it has half the frequency.

    Knowing that, the graph can be drawn using cos\theta to guide.
    Attached Thumbnails Attached Thumbnails GRAPH OF COSine FUNCTION-cosine.jpg  
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