Question 6.3.5: Rectangular-to-Polar Point Conversion Find polar coordinates...

We begin with (x, y) = (-2, 0) and find a set of polar coordinates (r, θ).

Step 1   Plot the point (x, y). The point (-2, 0) is plotted in Figure 6.27.

Step 2  Find r, the distance from the origin to (x, y). Can you tell by looking at Figure 6.27 that this distance is 2?

r=\sqrt{x^2+y^2}=\sqrt{(-2)^2+0^2}=\sqrt{4}=2.

Step 3 Find θ with θ lying on the same positive or negative axis as (x, y). The point (-2, 0) is on the negative x-axis. Thus, θ lies on the negative x-axis and θ = π. One representation of (-2, 0) in polar coordinates is (2, π).