Calculus

Find the length of the entire perimeter of the region inside
r = 16sin(theta) but outside r = 4.

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1. First define the region. Drawing a sketch chould help.

16 sin*theta = 4 when
theta = arcsin 1/4
which cporresponds to 14.48 degrees and 165.52 degrees

Your region is the area bounded by 16 sin(theta) on the outside and r = 4 on the inside. The outer curve is called a cardioid, as I recall. There is a fomula for the arc length of a cardioid at
http://en.wikipedia.org/wiki/Cardioid

The length of the circular arc is trivial. You will need to keep theta in radians.

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posted by drwls
2. 20*(2.888912398 - .25268002551)

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3. 64π

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posted by mariel

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