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.
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
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.