Polar Graphing – Extra Practice / Review
Name
Equation
Line passing through the pole
with a slope of 𝐭𝐚𝐧 𝑲
𝜃=𝐾
𝑟 = acos 𝜃 + 𝑏 sin 𝜃
Circle
𝑟 = acos 𝜃
𝑟 = bsin 𝜃
𝑟 = 𝑎 + 𝑏𝜃
Spiral
𝑟 = 𝑎 ± 𝑎 cos 𝜃
Cardioid
𝑟 = 𝑎 ± asin 𝜃
Example
𝑟 = 𝑎 ± 𝑏 cos 𝜃, 𝑏 > 𝑎
𝑟 = 𝑎 ± 𝑏 sin 𝜃, 𝑏 > 𝑎
Limaçon
𝑟 = 𝑎 ± 𝑏 cos 𝜃, 𝑎 > 𝑏
𝑟 = 6 + 4 cos 𝜃
𝑟 = 𝑎 ± 𝑏 sin 𝜃, 𝑎 > 𝑏
𝑟 = acos(𝑛𝜃)
Rose
𝑟 = asin(𝑛𝜃)
Note on Rose Curves:
Even more interesting graphs emerge when the
coefficient of is not an integer. For example, if it
is rational, then the curve is closed; that is, it
eventually ends where it started the curve is
closed However, if the coefficient is irrational,
then the curve never closes.
𝑟 ! = 𝑎! cos(2𝜃)
Lemniscate
𝑟 ! = 𝑎! sin(2𝜃)
𝑟 ! = 36 cos(2𝜃)
𝑟 = 3 sin(𝜃)
𝑟 = 3 sin(𝜃)
𝑟 = 4 cos(𝜃)
𝑟 = 4 cos(𝜃)
𝑟 = 2 cos(2𝜃)
𝑟 = 2 sin(2𝜃)
𝑟 ! = 4 sin(2𝜃)
𝑟 ! = 4 cos(2𝜃)
𝑟 = 1 + 2 cos 𝜃
𝑟 = 1 + 2 sin 𝜃
𝑟 = 2.5 + 2.5 sin 𝜃
𝑟 = 2.5 + 2.5 cos 𝜃
𝑟 = 3𝜃