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 y^{2} = x^{3} to polar equation.
Choices:
A. r = tan^{2} ? sec ?B. r = tan^{2} ?
C. r2 = tan^{2} ? sec ?
D. r = cot^{2} ? cos ?
Correct Answer: A
Solution:

Step 1: y^{2} = x^{3} [Rectangular equation.]
Step 2: (rsin ?)^{2} = (rcos ?)^{3} [Use y = rsin ? and x = rcos ?]
Step 3: r^{2}sin^{2}? = r^{3}cos^{3} ?
Step 4: sin^{2} ? / cos^{3} ? = r^{3}/ r^{2}
Step 5: r = tan^{2} ? sec ? [Use trigonometric definitions.]
Step 6: So, the polar equation is r = tan^{2} ? sec ?.
Translate :