CFU polar functions

What is r

radius

what is theta

direction

How to convert rectangular to polar

r=√x²+y² and tan^-1(y/x)=theta

How to convert real complex to polar

(a+ib) a=x b=y r=√x²+y² and tan^-1(y/x)=theta

What is the rule when convert rectangular or real complex to polar

identify the quadrant of rec or real complex

How to convert polar to rectangular

x=rcostheta y=rsintheta

How to convert polar to real complex

(a+ib) a=x b=y x=rcostheta y=rsintheta

Circles

r=acos(theta) r=asin(theta)

a can be both greater than or less than theta

Cardiod

r=a±bcos/sin(theta) a=b

One-Loop/dimpled Limacon

r=a±bcos/sin(theta) a>b

Inner-Loop Limacon

r=a±bcos/sin(theta) a<b

Lemniscate

r²=±a²cos/sin(2theta) a≠0

Rose

r=±acos/sin(ntheta) a≠0

Rule about n

when n is even its 2n when its odd it only n

Archimedes sprial

r=theta

Increasing

r is positive and increasing

r is negative and decreasing

Decreasing

r is positive and decreasing

r is negative and increasing

AROC

m=(r(theta2)-r(theta1))/(theta2-theta1)

Approximation

r(theta2)=r(theta1)+m(theta2-theta1)