Start by finding r at the endpoints. When θ = 0,r = cos0 = 1.
As θ moves from 0 to , the value of r = cos θ decreases from 1 to 0.
When , r = 0.
When θ = π, r = cosπ = -1.
Remembering how we graph polar coordinates with negative r, we find these points:
When θ is in the second quadrant and r is negative, the point (r,θ) is in the fourth quadrant.As θ moves closer to π, the points (r,θ) move closer to the positive x-axis.
As θ moves from to π, the value r = cosθ goes from 0 to -1.
The points (r,θ) move further from the origin as θ gets closer to π.
To graph r = cosθ for 0≤ θ≤ π we put the graphs from (a) and (b) together: