What's the total arc length of r=3sinθ?

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Answer 1 · 2018-03-11T18:32:52

#6pi# units.

#r=3sintheta#
#r^2=9sin^2theta#

#r'=3costheta#
#(r')^2=9cos^2theta#

Arc length is given by:

#L=int_0^(2pi)sqrt(9sin^2theta+9cos^2theta)d theta#

Simplify:

#L=3int_0^(2pi)d theta#

Hence

#L=6pi#