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Graphing Other Common Polar Equations definitions

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  • Cardioid
    A heart-shaped polar graph formed when coefficients of cosine or sine are equal in the equation r = a ± b cos(θ) or r = a ± b sin(θ).
  • Limaçon
    A polar graph with a dimple or inner loop, created when coefficients a and b in r = a ± b cos(θ) or r = a ± b sin(θ) are unequal.
  • Rose
    A flower-like polar graph with multiple petals, described by r = a cos(nθ) or r = a sin(nθ), where n determines petal count.
  • Lemniscate
    A figure-eight or infinity-shaped polar graph, defined by r² = ±a² cos(2θ) or r² = ±a² sin(2θ), unique for its squared r term.
  • Polar Axis
    The reference line in polar coordinates, analogous to the x-axis, often used to determine symmetry in polar graphs.
  • Quadrantal Angles
    Key angles in polar coordinates: 0, π/2, π, and 3π/2, used for plotting points when graphing polar equations.
  • Symmetry
    A property of polar graphs indicating reflection over the polar axis, θ = π/2, or the pole, based on the equation's form.
  • Inner Loop
    A feature of some limaçons where the graph passes through the pole, occurring when coefficient b exceeds a.
  • Dimple
    A slight indentation in a limaçon graph, present when coefficient a is greater than b, without forming an inner loop.
  • Petal
    One of the repeated lobes in a rose or lemniscate graph, with number and spacing determined by the equation's parameters.
  • Pole
    The origin point in polar coordinates, serving as the center from which distances (r) are measured.
  • Coefficient
    A numerical factor (a or b) in polar equations that influences the size, shape, and features of the graph.
  • Parameter n
    An integer in rose equations that determines the number of petals; even n yields 2n petals, odd n yields n petals.
  • Addition or Subtraction
    A distinguishing feature in cardioid and limaçon equations, indicating the presence of both a and b terms.
  • Squared r Term
    A unique aspect of lemniscate equations, where r is squared, making these graphs easily identifiable among polar equations.