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Convert Points Between Polar and Rectangular Coordinates definitions

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  • Polar Coordinates
    A system representing points by a distance from the origin and an angle from the positive x-axis.
  • Rectangular Coordinates
    A system representing points by horizontal (x) and vertical (y) distances from the origin.
  • Radius
    The distance from the origin to a point in the polar coordinate system, often denoted as r.
  • Angle
    The measure, usually in radians or degrees, from the positive x-axis to the line connecting the origin to a point.
  • Hypotenuse
    The longest side of a right triangle, corresponding to the radius in polar coordinates.
  • Unit Circle
    A circle with radius 1 centered at the origin, used as a reference for trigonometric values.
  • Cosine Function
    A trigonometric function relating the adjacent side to the hypotenuse in a right triangle.
  • Sine Function
    A trigonometric function relating the opposite side to the hypotenuse in a right triangle.
  • Tangent Function
    A trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle.
  • Inverse Tangent
    A function used to determine the angle whose tangent is a given value, often needed for coordinate conversion.
  • Pythagorean Theorem
    A geometric principle stating that the sum of the squares of the legs equals the square of the hypotenuse.
  • Quadrant
    One of four regions in the coordinate plane, determined by the signs of x and y values.
  • Origin
    The point (0,0) in rectangular coordinates or r = 0 in polar coordinates, serving as the reference point.
  • Quadrantal Angle
    An angle whose terminal side lies along the x-axis or y-axis, such as 0, π/2, π, or 3π/2 radians.
  • Coordinate System
    A method for uniquely identifying points in a plane using numbers, such as polar or rectangular formats.