Plot the given point in rectangular coordinates

Question

Plot the given point in rectangular coordinates and find two sets of polar coordinates for the point for 0 ≤ Θ ≤ 2π.

1. (-7, 0)

Answer 1

The point (-7, 0) lies on the negative x-axis, 7 units from the origin. To find polar coordinates (r, θ), use the formula r = sqrt(x^2 + y^2) = sqrt((-7)^2 + 0^2) = sqrt(49) = 7. To find θ, use the formula tan(θ) = y/x = 0/(-7) = 0. There are two solutions to this equation in [0, 2π], namely θ = 0, π, but since the point is on the negative x-axis, it has to be θ = π (θ = 0 gives the positive x-axis). To find another θ, just add 2π to the original θ = π.