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Math Help - Sketching polar graph

  1. #1
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    Sketching polar graph

    Sketch the curve r = 2cos4\theta

    Attempt:

    when \theta = 0, r = 2

    when \theta = \frac{\pi}{6}, r = -1

    when \theta = \frac{\pi}{4}, r = -2

    The graph I got was a circle (not ment to look like an ellipse in the drawing), but the correct answer was a flower
    Attached Thumbnails Attached Thumbnails Sketching polar graph-polar.jpg  
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by SyNtHeSiS View Post
    Sketch the curve r = 2cos4\theta

    Attempt:

    when \theta = 0, r = 2

    when \theta = \frac{\pi}{6}, r = -1

    when \theta = \frac{\pi}{4}, r = -2

    The graph I got was a circle (not ment to look like an ellipse in the drawing), but the correct answer was a flower
    You need more points.

    Hint: Find the points where r=0.
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  3. #3
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    Hello, SyNtHeSiS!

    \text{Sketch the curve: }\;r \:=\: 2\cos4\theta

    We are expected to recognize this as a "rose curve", a flower-shaped curve.
    . . [But it looks more like a daisy.]

    There are two basic forms: . \begin{Bmatrix}r &=& a\sin n\theta \\ r &=& a \cos n\theta \end{Bmatrix}

    \,a is the length of a "petal".

    If \,n is odd, there are \,n petals.
    If \,n is even, there are 2n petals.
    . . The petals are equally spaced about the center.


    We have: . r \:=\:2\cos4\theta

    Since n = 4 (even), there are 8 petals, spaced 45 degrees apart.
    Each petal is 2 units long.


    Now where are the petals?
    . . When is r = 2 ?

    We have: . 2\cos4\theta \:=\:2 \quad\Rightarrow\quad \cos4\theta \:=\:1 \quad\Rightarrow\quad 4\theta \:=\:\cos^{\text{-}1}(1)

    . . . . . . . . 4\theta \:=\:0^o \quad\Rightarrow\quad \theta\:=\:0^o

    Hence, the "first" petal is on the 0^o-line (positive \,x-axis).


    You should be able to sketch the graph now.

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