Table 8-3 Common Polar Equations and Their Graphs Lines 6 = 0 0 = 0 x-axis 8 = a r= r= 0 = ~y-axis Line through origin sin 8 cos Horizontal line (y = a) Vertical line (x = a) Circles and Spirals = 3sine r = 3cose r= 0.50 r = a r = acos e r = asin e r = a0 Circle: center at the Circle: center on polar Circle: center on / = Spiral pole, radius lal axis, radius radius Limacons r = a t bcos 0 r = at bsin d r= 3+2cose = 1 + 2cose r = 1 + cose F = 2 + cos0 (a > 0, b > 0) The orientation and - 0 symmetry depend on the trigonometric function and the sign of the sine or cosine term. a 2b limacon with a loop cardioid dimpled limacon convex limaconRoses r = acos ne F = 3sin 20 F = 3sin40 r = asin ne r = 3sin 30 - 3sin 50 n petals if n is odd 2n petals n is even 0 0 r = asin 20 r = asin 40 r = asin 30 r = asin 50 4-petal rose 8-petal rose 3-petal rose 5-petal rose Lemniscates 12 = a2 cos 20 12 = asin 20 72 = 9sin 20 12 = 9cos20 Figure-eight symmetric to the polar axis (cosine) or symmetric to the line 0 = = (sine) 12 = a- cos 20 12 = a sin 20 figure-eight figure-eight\f