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
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
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
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
2sin
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.