Sketching Curves in Polar Coordinates

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If you want to sketch a curve expressed in polar formthere are some elementary things to remember.

  1. cannot be negative! If some value ofgives a negative value forthe curve is not defined there.
  2. is the angle the radius vector makes with the positive– axis in a clockwise sense.
  3. Ifis a function ofthen the curve will havepetals, because asincreases from 0 toequivalent to one rotation about the origin,increases from 0 to giving rise to one petal for each increases ofby
  4. The maximum value ofis often whenoris 1, 0 or -1.

The graphis a maximum whenThe curve has 4 petals.

The cardioid– whenis max and whenWhen

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