How to draw polar graphs without using calculator.

I know how to draw these types as I know the rules and using only 0,90,180,270 forrI can graph whole thing.

a)r = a + bcos(theta) or r = a + bsin(theta)Limacons

and

b)r = asin(n theta) or r = acos (n theta)Roses

where a and b are integers

ButI dont how to do these ones.

whenr = a + cos(b theta)orr = a + sin(b theta)

Is there any rules/tricks for that. The only thing left in my opinion is using pi's and I dont want to use it.

ANY HELP IS APPRECIATED