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Polar Coordinate System definitions

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  • Polar Coordinate System
    A method for locating points using a distance from a central point and an angle from a fixed direction.
  • Pole
    The central reference point in this system, corresponding to the origin in rectangular coordinates.
  • Polar Axis
    The fixed reference line from which angles are measured, analogous to the positive x-axis.
  • Radius
    The distance from the pole to a point, represented by the variable r in this coordinate system.
  • Theta
    The angle measured from the polar axis to a point, typically in radians and measured counterclockwise.
  • Ordered Pair
    A notation (r, θ) representing a point's distance from the pole and its angle from the polar axis.
  • Coterminal Angles
    Angles that share the same terminal side, differing by multiples of 2π, and represent the same direction.
  • Reflection
    A transformation involving a negative value for r or θ, resulting in a point mirrored over the pole or axis.
  • Unit Circle
    A circle with radius 1, often used as a reference for measuring angles and understanding coterminal positions.
  • Rectangular Coordinates
    A system using x and y values to locate points, serving as a contrast to the polar method.
  • Quadrant
    One of four regions divided by the polar axis and its perpendicular, used to describe point locations.
  • Negative Radius
    A value for r that requires plotting a point in the direction opposite to the given angle.
  • Negative Angle
    A value for θ indicating measurement in the clockwise direction from the polar axis.
  • Multiple Representations
    The concept that a single point can be described by various (r, θ) pairs due to angle and radius properties.
  • Interval
    A specified range for r or θ, often used to restrict possible representations of a point.