Example 1: Ploting Points

Plot the following points in polar coordinates.

(2, π/4), (-1, π/4), (3,3 π/4), (2, -π/4), (-4, -π/4).

The solution is shown in Figure 7.7.3.

Each point P has infinitely many different polar coordinate pairs. We see in Figure 7.7.4 that the point P(3, π/2) has all the coordinates

(3, π/2 + 2nπ),

n an integer. (-3,3 π/2 + 2nπ),

Figure 7.7.3 Figure7.7.4

Figure 7.7.5

Any coordinate pair (0, θ) with r = 0 determines the origin. As we see in Figure 7.7.5, the coordinates of a point P in rectangular and in polar coordinates are related by the equations

x = r cos θ, y = r sin θ.

The graph, or locus in polar coordinates of a system of formulas in the variables r, θ is the set of all points P(r, θ) for which the formulas are true.