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Thread: GRAPH OF COSine FUNCTION

  1. #1
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    GRAPH OF COSine FUNCTION

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

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

    $\displaystyle y=2-\mid cos\frac{\theta}{2}\mid$
    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 $\displaystyle 0<\theta<2\pi$

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

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

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

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

    or it has half the frequency.

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