009C Sample Final 1, Problem 8

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A curve is given in polar coordinates by

a) Sketch the curve.
b) Find the area enclosed by the curve.

The area under a polar curve is given by
for appropriate values of



Step 1:  
009C SF1 8.jpg


Step 1:  
Since the graph has symmetry (as seen in the previous image), the area of the curve is
Step 2:  
Using the double angle formula for we have
Step 3:  
Lastly, we evaluate to get
Final Answer:  
   (a) See Step 1 above.

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