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Graphing Other Common Polar Equations definitions

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  • Polar Equation
    Mathematical expression involving R, theta, and trigonometric functions, used to describe curves in polar coordinates.
  • Cardioid
    Heart-shaped curve formed when A and B are equal in the equation R = A ± B cos(theta) or R = A ± B sin(theta).
  • Limaçon
    Curve with a dimple or inner loop, defined by A ≠ B in R = A ± B cos(theta) or R = A ± B sin(theta).
  • Rose
    Flower-like curve with multiple petals, described by R = A cos(N*theta) or R = A sin(N*theta), where N ≥ 2.
  • Lemniscate
    Infinity-shaped curve defined by R² = ± A² cos(2*theta) or R² = ± A² sin(2*theta), unique for its squared R.
  • Petal
    Distinct loop or segment in rose or lemniscate graphs, whose number and placement depend on N and symmetry.
  • Symmetry
    Characteristic of a graph indicating reflection about the polar axis or specific lines, determined by the equation's trigonometric function.
  • Polar Axis
    Reference line in polar coordinates, analogous to the positive x-axis, used for symmetry and plotting.
  • Quadrantal Angle
    Angles at 0, π/2, π, and 3π/2, crucial for plotting key points in polar graphs.
  • Inner Loop
    Feature in a limaçon graph appearing when A < B, causing the curve to pass through the pole.
  • Dimple
    Indentation in a limaçon graph occurring when A > B, resulting in a curve without an inner loop.
  • Pole
    Origin in polar coordinates, central point from which curves radiate or reflect.
  • Trigonometric Function
    Cosine or sine function used in polar equations to define the shape and orientation of curves.
  • Integer N
    Parameter in rose equations determining the number of petals; must be ≥ 2.
  • Continuous Curve
    Smooth connection of plotted points in polar graphs, ensuring the shape is accurately represented.