Types of Polar Functions

straight line.

cos is a vertical line in x=a

sin is a horizontal line in y=a

circles

cos circles are centered on the x axis w/ diameter a

sin circles are centered on the y axis w/ diameter a

Cardioloids (Hearts)

a + acos: go right a+a, up&down a

a - acos: go left a+a, up&down a

a + asin: go up a+a, right&left a

a - asin: go down a+a, right&left a

Dimpled Limaçons (No loop; semi-heart)

a + acos: go right a+b, left a-b, up/down a

a - acos: go left a+b, right a-b, up/down a

a + asin: go up a+b, down a-b, right/left a

a - asin: go down a+b, up a-b, right/left a

Limaçons with loop

a + acos: go right a+b (outer loop), right a-b (inner loop), up/down a

a - acos: go left a+b (outer loop), left a-b (inner loop), up/down a

a + asin: go up a+b (outer loop), up a-b (inner loop), right/left a

a - asin: go down a+b (outer loop), down a-b (Inner loop), right/left a

Roses

each petal is a radiuses long

when n is odd, there will be n petals

when n is even, there are 2n petals

each petal is 2pi/#petals apart