Polar Coordinates

(requires JavaScript)

  1. Sketch the region in the plane consisting of points whose polar coordinates satisfy 1r1 and π4θ3π4 .

  2. Find a polar equation for the curve represented by the Cartesian equation

    x2+y2=2cx

    r=2ccosθ
  3. Sketch the curve given by r=sinθ .
    A circle through the origin and 1π2 .
  4. Sketch the curve given by r=2cos4θ .
  5. Match the polar equations with the graphs without using a computer. Explain.

    1. r=sinθ2
    2. r=sinθ4
    3. r=1cos3θ
    4. r=θsinθ
    5. r=1+4cos5θ
    6. r=1θ

    polar curve (a) polar curve (b)

    polar curve (c) polar curve (d)

    polar curve (e) polar curve (f)