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 n? or r = a cos n? is n, if n is odd, and 2n, if n is even, where a is constant.
  • If the polar equation is r(- ?) = r(?), then the curve is symmetrical about the horizontal axis.
  • If the polar equation is r(p - ?) = r(?), then the curve is symmetrical about the vertical axis.

Video Examples: Graphing a Polar Equation - Algebra Tips


Example of Polar Equation

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

Solved Example on Polar Equation

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

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

Solution:

    Step 1: y2 = x3 [Rectangular equation.]
    Step 2: (rsin ?)2 = (rcos ?)3 [Use y = rsin ? and x = rcos ?]
    Step 3: r2sin2? = r3cos3 ?
    Step 4: sin2 ? / cos3 ? = r3/ r2
    Step 5: r = tan2 ? sec ? [Use trigonometric definitions.]
    Step 6: So, the polar equation is r = tan2 ? sec ?.