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Polar Coordinates definitions

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  • Polar Coordinate System
    A plane system where points are determined by a distance from a central pole and an angle from a fixed axis.
  • Pole
    The central reference point in polar coordinates, analogous to the origin in rectangular coordinates.
  • Polar Axis
    The fixed reference line from which angles are measured in polar coordinates, similar to the positive x-axis.
  • 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, found by adding or subtracting multiples of 2π.
  • Rectangular Coordinates
    A system using (x, y) pairs to locate points based on horizontal and vertical distances from the origin.
  • Conversion Equations
    Formulas x = r cos(θ) and y = r sin(θ) used to switch between polar and rectangular coordinates.
  • Pythagorean Theorem
    A relationship used to find the radius in polar form: r² = x² + y².
  • Tangent Function
    A trigonometric ratio used to find the angle in polar form: tan(θ) = y/x.
  • Cardioid
    A heart-shaped polar graph with equation r = a ± a cos(θ) or r = a ± a sin(θ).
  • Limacon
    A polar graph with equation r = a ± b cos(θ) or r = a ± b sin(θ), where a ≠ b, producing dimples or loops.
  • Rose
    A polar graph with petal patterns, given by r = a cos(nθ) or r = a sin(nθ), where n determines petal count.
  • Lemniscate
    A figure-eight shaped polar graph with equation r² = a² cos(2θ) or r² = a² sin(2θ).
  • Symmetry
    A property indicating whether a polar graph mirrors across the polar axis, θ = π/2, or the pole.
  • Quadrantal Angles
    Key angles (0, π/2, π, 3π/2) used for plotting and analyzing points in polar graphs.