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Graphing Other Common Polar Equations quiz

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  • What is the general equation form for both cardioids and limaçons in polar coordinates?
    The general form is r = a ± b cos(θ) or r = a ± b sin(θ).
  • How do you distinguish a cardioid from a limaçon based on the values of a and b?
    A cardioid has a = b, while a limaçon has a ≠ b.
  • What feature does a limaçon have if a > b?
    The limaçon will have a dimple but no inner loop.
  • What is the equation form for a rose curve in polar coordinates?
    A rose curve has the form r = a cos(nθ) or r = a sin(nθ), where n ≥ 2.
  • How do you determine the number of petals in a rose curve when n is even?
    The number of petals is 2n when n is even.
  • What is the unique feature of the lemniscate equation compared to other common polar equations?
    The lemniscate equation contains r squared, as in r² = ±a² cos(2θ) or r² = ±a² sin(2θ).
  • How do you determine symmetry for a cardioid with a cosine function?
    The graph is symmetric about the polar axis.
  • When graphing a cardioid, at which angles should you plot key points?
    Plot points at the quadrantal angles: 0, π/2, π, and 3π/2.
  • If a limaçon equation contains a sine function, about which line is it symmetric?
    It is symmetric about the line θ = π/2.
  • How do you find the length of each petal in a rose curve?
    The length of each petal is equal to the value of a in the equation.
  • What is the first step in graphing a lemniscate?
    Find the value of a by taking the square root of the coefficient of the trigonometric function.
  • How do you graph the second petal of a lemniscate after finding the first?
    Reflect the first petal over the pole (origin) to locate the second petal.
  • What does the presence of addition or subtraction in a polar equation indicate about the shape?
    It indicates the equation is for a cardioid or a limaçon.
  • How do you determine the spacing between petals in a rose curve?
    Divide 2π by the number of petals to find the angular spacing.
  • What general shape does a lemniscate resemble when graphed?
    A lemniscate resembles an infinity symbol or a propeller with two petals.