Definition of Polar Coordinates

Polar coordinates express the location of a point as (r, θ), where r is the distance from the origin to the point and θ is the angle from the positive x-axis to the point (in degrees or radians). The distance r is also the hypotenuse of the right triangle formed using the x-axis. Using the Pythagorean Theorem and trigonometric functions, and . When graphing polar coordinates, the same point can represent several sets of coordinates. For example, θ = 60° and θ = 420o will return the same point for a given value of r (because 420° = 360° + 60°). Additionally, (r, θ) is the same as (-r, θ + 180° or π rad), because the negative sign indicates movement in the opposite direction.

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