Page 53 - Calculus for the Clueless, Calc II
P. 53
Rule 4
Symmetries to aid polar curve sketching: *
A. x-axis sym. If replacing (r,θ) by (r,θ) or (-r,π - θ) gives the same or equivalent equation.
B. y-axis sym. If replacing (r,θ) by (-r,-θ) or (r,π - θ) gives the same or equivalent equation.
C. Origin sym. If replacing (r,θ) by (-r,θ) or (r,π + θ) gives the same or equivalent equation.
There are several curves that you should know by looking at the equation. It is always easier to sketch a curve if
you know what it looks like before you start.
Rule 5
Circles tangent to origin, radius |a|/2, x- or y-axis is the axis of symmetry.
Rule 6
Cardioid:
* Two of the symmetries mean all three hold.
