Graphing Polar Equations

Identifying a Cardioid

|a|/|b| = 1

Identifying One-Loop (dimpled) Limacons

|a| > |b|

Identifying Looped Limacons

|a| < |b|

Equation for Limacons

r = a ± b cos/sin(theta)

Finding x-intercepts for Limacons (in the case of positive cos)

Add a and b values for outer x-intercept, subtract b from a for inner, if applicable

Finding y-intercepts for Limacons (in case of positive cos)

Focus on a-value

Finding x and y intercepts for Sine Limacons

Formulas are the same, but inversed (if you’re finding y in cos, its for x in sine)

Finding x and y Intercepts for Negative Trig Graphs

Mirror the values (if you had 5 as one of your intercepts, it becomes -5)

Equation for Rose-Shaped Polar Graphs

r = cos/sin(b * theta)

Number of Petals

Given r = a cos(b * theta), number is equal to b-value with odd numbers, doubled in even ones.

Cosine vs Sine Rose Graphs

A petal will always be in the center of the x-axis with cosine equations

Polar Equation for Circles

r = a cos theta