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


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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 values: (x, y). The x-coordinate indicates the horizontal position, while the y-coordinate indicates the vertical position. The conversion from polar to rectangular coordinates involves using the formulas x = r * cos(θ) and y = r * sin(θ).

Conversion between Polar and Rectangular Coordinates

To convert polar coordinates to rectangular coordinates, one must apply trigonometric functions based on the angle provided. For a point given in polar form (r, θ), the rectangular coordinates can be calculated as x = r * cos(θ) and y = r * sin(θ). This process is crucial for solving problems that require the use of rectangular coordinates instead of polar ones.