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Convert Points Between Polar and Rectangular Coordinates definitions

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  • Polar Coordinates
    A system representing points by distance from the origin and angle from the positive x-axis, useful for circular and rotational contexts.
  • Rectangular Coordinates
    A system representing points by horizontal and vertical distances from the origin, commonly used in Cartesian graphs.
  • Hypotenuse
    The longest side of a right triangle, connecting the origin to a point in polar coordinates and used to calculate r.
  • Unit Circle
    A circle with radius 1 centered at the origin, foundational for understanding trigonometric relationships in coordinate conversions.
  • Cosine
    A trigonometric function relating the adjacent side to the hypotenuse, used to find the x-component in conversions.
  • Sine
    A trigonometric function relating the opposite side to the hypotenuse, used to find the y-component in conversions.
  • Inverse Tangent
    A function used to determine the angle from the ratio of y to x, essential for finding θ in polar coordinates.
  • Quadrant
    One of four regions in the coordinate plane, important for adjusting angles during conversions between systems.
  • Pythagorean Theorem
    A formula relating the sides of a right triangle, used to calculate the distance r from x and y values.
  • Quadrantal Angle
    An angle located on the axes, such as 0, π/2, π, or 3π/2, relevant when points lie directly on x or y axes.
  • Origin
    The central point (0,0) in both coordinate systems, corresponding to r = 0 in polar coordinates.
  • Angle θ
    The measure from the positive x-axis to the line connecting the origin to the point, crucial for polar representation.
  • Radius r
    The distance from the origin to a point, forming the hypotenuse in the triangle used for conversions.
  • Decimal Form
    A numerical representation used for easier plotting and visualization of coordinates on graphs.
  • Coordinate System
    A framework for locating points, either by (x, y) or (r, θ), enabling conversion and comparison between representations.