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