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Exercises

  1. For each of the following polar equations, plot the graph in polar coordinates using the plot command and identify the graph as a cardioid, limaçon, or rose.
    A)
    $r = \frac{1}{2}\sin(5 \theta)$
    B)
    $r = 2 -3 \cos(\theta)$
    C)
    $r = 2 + 2\sin(\theta-Pi/4)$

  2. Find all points of intersection for each pair of curves in polar coordinates.
    A)
    $r = 2-\cos(\theta)$ and $r=2 \sin(\theta)$
    B)
    $r=1+2\cos(\theta)$ and $r=\cos(3 \theta)$
  3. A)
    Plot the polar equation $r=1+3\cos(\theta)$. Find the angles that create the inner loop of $r=1+3\cos(\theta)$. Plot only the inner loop and then find the area inside the inner loop.
    B)
    Plot only one petal of the rose in exercise 1A and find the area of this petal.


Dina J. Solitro-Rassias
2015-11-12