Question

What are the intersection points for r = 1 cos(θ) and r = 1 - cos(θ)?

A) (π/3, √3/2) and (5π/3, √3/2)
B) (π/2, 0) and (3π/2, 0)
C) (π/3, √3/2) and (4π/3, √3/2)
D) (π, -1) and (2π, -1)

Answer 1

The intersection points for r = 1 cos(θ) and r = 1 - cos(θ) are (π/3, √3/2) and (5π/3, √3/2).

Step-by-step explanation:

To find the intersection points for r = 1 cos(θ) and r = 1 - cos(θ), we can set the two equations equal to each other:

1 cos(θ) = 1 - cos(θ)

Simplifying the equation:

2 cos(θ) = 1

cos(θ) = 1/2

θ = π/3, 5π/3

Substituting the values of θ back into the equation for r:

r = 1 cos(π/3) = 1(1/2) = 1/2

r = 1 cos(5π/3) = 1(1/2) = 1/2

The intersection points are (π/3, √3/2) and (5π/3, √3/2), so the correct answer is (A) (π/3, √3/2) and (5π/3, √3/2).