Polar Equation

Definition of Polar Equation

An equation of a curve in terms of polar coordinates r and ? is called a Polar Equation.

More About Polar Equation

  • The number of petals in the graph of a polar equation r = a sin nθ or r = a cos nθ is 'n', if n is odd, and '2n', if n is even, where 'a' is constant.
  • If the polar equation is r(- θ) = r(θ), then the curve is symmetrical about the horizontal axis.
  • If the polar equation is r(π - θ) = r(θ), then the curve is symmetrical about the vertical axis.

Video Examples: Graphing a Polar Equation - Algebra Tips

Example of Polar Equation

    r = 3sin 4θ and r = 2cos 5θ are polar equations as they are written in terms of r and θ.

Solved Example on Polar Equation

Ques: Convert the rectangular equation y2 = x3 to polar equation.

    A. r = tan2 θ sec θ
    B. r = tan2 θ
    C. r2 = tan2 θ sec θ
    D. r = cot2 θ cos θ
    Correct Answer: A


    Step 1: y2 = x3 [Rectangular equation.]
    Step 2: (rsin θ)2 = (rcos θ)3 [Use y = rsin θ and x = rcos θ]
    Step 3: r2sin2θ = r3cos3 θ
    Step 4: sin2 θ / cos3 θ = r3/ r2
    Step 5: r = tan2 θ sec θ [Use trigonometric definitions.]
    Step 6: So, the polar equation is r = tan2 θ sec θ.

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