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. (3, 4π/3)

Key Concepts

Polar Coordinates

Polar coordinates represent points in a plane using a distance from a reference point (the pole) 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. This system is particularly useful for circular and rotational problems.

Plotting Points in Polar Coordinates

To plot a point given in polar coordinates, first identify the radial distance 'r' and the angle 'θ'. The angle is measured counterclockwise from the positive x-axis. For example, for (3, 4π/3), you would move 3 units away from the origin at an angle of 240 degrees (or 4π/3 radians), which places the point in the third quadrant.

Conversion Between Polar and Cartesian Coordinates

Understanding how to convert between polar and Cartesian coordinates is essential. The conversion formulas are x = r * cos(θ) and y = r * sin(θ). This allows you to translate polar coordinates into the familiar (x, y) format, facilitating easier plotting and analysis in a Cartesian plane.