Cardioid

03 Area Enclosed by Cardioids: r = a(1 + sin θ); r = a(1 - sin θ), r = a(1 + cos θ), r = a(1 - cos θ)

Problem
Find the area individually enclosed by the following Cardioids:
(A)   $r = a(1 - \cos \theta)$
(B)   $r = a(1 + \cos \theta)$
(C)   $r = a(1 - \sin \theta)$
(D)   $r = a(1 + \sin \theta)$
 

003-cardioid-neg-pos-sine-cosine.gif

 

Perimeter of the curve r = 4(1 + sin theta) by integration

Problem
What is the perimeter of the curve r = 4(1 + sin θ)?
 

cardioid-pointing-upward.jpg

 

The answer is 32 units. For detailed solution, follow the link by clicking on the figure.
 

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