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    Polar Coordinates

    Illustration

    Illustration

    Alternate name

    polar coordinate system

    Basic definition

    Polar coordinates are a two-dimensional coordinate system in which points in two dimensions are given by an angle and a distance from the origin.

    Detailed definition

    The polar coordinates r (the radial coordinate) and θ (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x | = | r cos θ y | = | r sin θ, where r is the radial distance from the origin, and θ is the counterclockwise angle from the x-axis. In terms of x and y, r | = | sqrt(x^2 + y^2) θ | = | tan^(-1)(y/x).

    Related terms

    Argand diagram | cardioid | circle | cissoid | complex argument | complex modulus | complex number | conchoid | curvilinear coordinates | cylindrical coordinates | Euler formula | lemniscate | limaçon | logarithmic spiral | polar angle | polar plot | polar vector | rose curve

    Educational grade level

    high school level (California trigonometry standard)

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