In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (−2, − π/2)

Key Concepts

Polar Coordinates

Polar coordinates represent points in a two-dimensional space using a distance from a reference point (the origin) and an angle from a reference direction (usually the positive x-axis). The format is (r, θ), where 'r' is the radial distance and 'θ' is the angle in radians. Understanding this system is crucial for plotting points accurately in polar graphs.

Negative Radius in Polar Coordinates

In polar coordinates, a negative radius indicates that the point is located in the opposite direction of the angle specified. For example, the point (−2, −π/2) means to move 2 units in the direction opposite to the angle of −π/2 (which points downward), effectively placing the point at (2, π/2) in the Cartesian coordinate system.

Conversion Between Polar and Cartesian Coordinates

To plot points in a Cartesian coordinate system, one can convert polar coordinates (r, θ) to Cartesian coordinates (x, y) using the formulas x = r * cos(θ) and y = r * sin(θ). This conversion is essential for visualizing polar points on a standard x-y graph, allowing for a better understanding of their positions relative to the axes.