Polar and Rectangular

Going to rectangular form

multiply by r

Going to polar form

divide by r

x = 5 (vertical line)

r = 5 sec theta

y = 3 (horizontal line)

r = 3 csc theta

y = x

tan theta = 1

y = 1/6x

cot theta = 6

x^2 + y^2 = 25 (circle at origin)

r = 5

(x - 8)^2 + (y - 10)^2 = 25 (circle not at origin)

r = 4 cos theta + 5 sin theta

y = -4x^2

r = 1/4 tan theta sec theta

x = y^2/5

r = 5 cot theta csc theta

polar axis

1st and 4th quadrant are the same

the line

1st and 2nd quadrant are the same

the pole

1st and 3rd quadrant are the same

lemniscates

r^2 = a^2 sin/cos 2 theta

circle

r = a sin/cos theta

rose curve

r = a sin/cos n theta

limacon

r = a +/- b sin/cos theta

cardiod

a = b

b < a < 2b

dimple limacon

a > 2b

convex limacon