GRAPHS OF SOME INTERESTING POLAR EQUATIONS

Example 1:

Go to desmos.com and in settings change from the rectangular to the polar grid. You must use on the desmos keyboard! Type r = 2 cos 3 and observe the graph.

The graph is a Rose Curve with 3 petals since 3 is odd.

Example 2:

Go to desmos.com and in settings change from the rectangular to the polar grid. You must use on the desmos keyboard! Type r = 2 cos 2 and observe the graph.

The graph is a Rose Curve with 4 petals since 2 is even.

Example 3:

Go to desmos.com and in settings change from the rectangular to the polar grid. You must use on the desmos keyboard! Type r = 1 + cos and observe the graph.

The graph is a heart-shaped Limacon also know as a Cardiod.

Example 4:

Go to desmos.com and in settings change from the rectangular to the polar grid. You must use on the desmos keyboard! Type r = 1 2sin and observe the graph.

The graph is a Limaçon with inner loop. Please note that .

Example 5:

Name the following limaçons:

a. r = 8 + 2 cos

Convex Limaçon because .

b. r = 3 + 2 sin

Dimpled Limaçon because .

c. r = 2 + 2 cos

Heart-Shaped Limaçon (Cardiod) because .

d. r = 2 + 3cos

Limaçon with Inner Loop because .

6. Find the number of petals of the Rose Curve with equation r = 2 sin (3).

The angle multiplier n = 4 is odd, therefore, this rose curve has 3 petals.

7. Find the number of petals of the Rose Curve with equation r = 2 cos (4) .

The angle multiplier n = 4 is even, therefore, this rose curve has 2(4) = 8 petals.

8. Give the equation of each circle graph with its equation.

a.

This is a circle with center along the polar axis. It has a radius of length 1. Therefore, its equation must be r = 2 cos.

b.

This is a circle with center at the pole. It has a radius of length 2. Therefore, its equation must be .

c.

This is a circle with center along the r-axis. It has radius of length 1.5. Therefore, its equation must be r = 3 sin.

9. Give the radius of each circle.

a. r = cos

This is a circle with center along the polar axis. Here, a = 1. It has a radius of length .

b. r = 10 cos

This is a circle with center along the r-axis. Here, a = 10. It has a radius of length which is 5.

c. r = 12

This is a circle with center at the pole. Here, a = 12. It has a radius of length 12.