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## Polar Equation Graphs

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**5 major kinds of Polar Graphs**• Circles r = a sin • Lamiconsr = a + b sin • Roses r = a sin (n • Archimedean Spiral r = a ± bθ • Lemniscates r2 = a2 sin 2**Circles**• General Form • r = a cosθ • r = a sin θ**Lamicons**r = a ± b cosθ or r = a ± b sin θ 3 scenarios a = b cardioids a > b dimpled a < b loopy**Cardioids (Lamicon)a = b**• General form r = a ± a cosθ or r = a ± a sin θ Basically a vaguely Heart shaped graph Can be an upside down or sideways heart. Always includes the origin**Lamiconsa > b**Does not ever Include the origin**Lamiconsa < b**Includes an Inner loop Always includes The origin**Roses**r = a cos bθ a determines radius b relates to the petals r = 3 cos 2θ**Archimedian Spiral**r = a ± bθ