Chapter 5 - Polar coordinates

what are polar coordinates

(r,θ)

how to find x coordinate from polar coordinate

how to find y coordinate from polar coordinate

how to find r²

how to find θ

polar graph r=a

circle with centre O and radius a

polar graph θ=α

half line through O and making an angle α with the inital line

polar graph r=aθ

spiral starting at O

r=acostheta

r=Asin theta

r=a+bcos theta when a/b<1

lemacon with loo

r=a+bcos theta when a/b=1

cardiod

r=a+bcos theta when 1<a/b<2

dimle

r=a+bcos theta when a/b>2

convex lemacon egg

what if -b

rotate 180

what if sin

rotate 90

a sin n\theta

acos ntheta

when n is off dumner

numer of petals is n

when n is even

2n numebr of petals

area of sector bounded by polar curve and the half lines theta=alpha and theta=beta where theta is in radians

tangent parallel to initial line set

Tangent perpendicular to initial line set