polar equation


Definition of Polar Equation

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

More about Polar Equation

  • The number of petals in the graph of a polar equation r = a sin or r = a cos 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.

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

Convert the rectangular equation y2 = x3 to polar equation.
Choices:
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
Solution:
Step 1: y2 = x3 [Rectangular equation.]
Step 2: (rsin θ)2 = (rcos θ)3 [Use y = rsin θ and x = rcos θ]
Step 3: r2sin2 θ = 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.

Related Terms for Polar Equation

  • Coordinates
  • Curve
  • Equation
  • Polar Form