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


(5 , ―60°)

Key Concepts

Polar Coordinates

Polar coordinates represent a point in a plane 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 how to interpret these coordinates is essential for converting them to rectangular coordinates.

Rectangular Coordinates

Rectangular coordinates, also known as Cartesian coordinates, express a point in a plane using two perpendicular axes, typically labeled x and y. The coordinates are given in the form (x, y). To convert from polar to rectangular coordinates, the formulas x = r * cos(θ) and y = r * sin(θ) are used, where 'r' is the radial distance and 'θ' is the angle.

Trigonometric Functions

Trigonometric functions, such as sine and cosine, are fundamental in converting polar coordinates to rectangular coordinates. The cosine function relates the adjacent side of a right triangle to the hypotenuse, while the sine function relates the opposite side to the hypotenuse. These functions are crucial for calculating the x and y values from the polar coordinates, especially when dealing with angles in degrees or radians.