GRAPHING POLAR CURVES r EQUAL TO COS THETA

The graph of the polar curve in the form

y = a cos θ

is a circle.

Where a is the diameter of the circle or the distance from the farthest point on the circumference.

The radius is |a|/2 or half the diameter.

If a > 0, then

If a < 0, then

Consider the polar equation. Classify the curve and sketch the graph.

Problem 1 :

r = 2 cos θ

Solution :

Type of polar graph : 

Comparing the given function with r = a cos θ, a = 2 > 0. Then, it is a circle with diameter of 2 units

Radius = 2/2

= 1 unit

Problem 2 :

r = 8 cos θ

Solution :

Type of polar graph : 

Comparing the given function with r = a cos θ, a = 8 > 0. Then, it is a circle with diameter of 8 units

Radius = 8/2

= 4 units

Problem 3 :

r = -5 cos θ

Solution :

Type of polar graph : 

Comparing the given function with r = a cos θ, a = -5 < 0. Then, it is a circle with diameter of 5 units

Radius = 5/2

= 2.5 units

Since the value of a is less than 0, we have to draw the circle to the left of x-axis.

Problem 4 :

r = -5 cos θ

Solution :

Type of polar graph : 

Comparing the given function with r = a cos θ, a = -5 < 0. Then, it is a circle with diameter of 5 units

Radius = 5/2

= 2.5 units

Since the value of a is less than 0, we have to draw the circle to the left of x-axis.