For each pair of polar coordinates, (c) give the rectangular coordinates for the point. See Examples 1 and 2(a).


(3 , 120°)

Key Concepts

Polar Coordinates

Polar coordinates represent a point 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 degrees or radians. Understanding this system is crucial for converting to rectangular coordinates.

Rectangular Coordinates

Rectangular coordinates, also known as Cartesian coordinates, express a point in a two-dimensional space using two values: (x, y). The x-coordinate indicates the horizontal position, while the y-coordinate indicates the vertical position. Converting from polar to rectangular coordinates involves using the formulas x = r * cos(θ) and y = r * sin(θ).

Trigonometric Functions

Trigonometric functions, such as sine and cosine, are fundamental in relating angles to the ratios of sides in right triangles. In the context of polar to rectangular conversion, these functions are used to determine the x and y coordinates based on the angle θ. Mastery of these functions is essential for accurately performing the conversion.