Sketching Curves in Polar Coordinates
If you want to sketch a curve expressed in polar formthere are some elementary things to remember.
cannot be negative! If some value ofgives a negative value forthe curve is not defined there.
is the angle the radius vector makes with the positive– axis in a clockwise sense.
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
The maximum value ofis often whenoris 1, 0 or -1.
The graph-is a maximum whenThe curve has 4 petals.
The cardioid– whenis max and whenWhen