**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! Typer = 2 cos 3and observe the graph.The graph is a

Rose Curvewith 3 petals sinceis odd.3

Example 2:

Go to desmos.com and in settings change from the rectangular to the polar grid. You must use

on the desmos keyboard! Typer = 2 cos 2and observe the graph.The graph is a

Rose Curvewith 4 petals sinceis even.2

Example 3:

Go to desmos.com and in settings change from the rectangular to the polar grid. You must use

on the desmos keyboard! Typer = 1 + cosand 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! Typer = 1 2sinand observe the graph.The graph is a

Limaçon with inner loop. Please note that .

Example 5:

Name the following limaçons:

a.

r = 8 + 2 cosConvex Limaçon because .

b.

r = 3 + 2 sinDimpled Limaçon because .

c.

r = 2 + 2 cosHeart-Shaped Limaçon (Cardiod) because .

d.

r = 2 + 3cosLimaçon with Inner Loop because .

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

The angle multiplier

n =is odd, therefore, this rose curve has4petals.3

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

The angle multiplier

is even, therefore, this rose curve hasn = 4petals.2(4) = 8

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 ber = 3 sin.

9. Give the radius of each circle.

a.

r = cosThis is a circle with center along the polar axis. Here,

. It has a radius of length .a = 1b.

r = 10 cosThis is a circle with center along the

r-axis. Here,. It has a radius of length which is 5.a = 10c.

r = 12This is a circle with center at the pole. Here,

. It has a radius of length 12.a = 12