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

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