Find the arc length of the astroid x(t)=cos^{3}t,\ y(t)=sin^{3}t

opatovaL 2021-09-05 Answered
Find the arc length of the astroid x(t)=cos3t, y(t)=sin3t.
Calculate the arc length of 14 of the astroid (0tπ2)
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Expert Answer

Theodore Schwartz
Answered 2021-09-06 Author has 99 answers

ds=(dxdt)2+(dydt)2
(dxdt)=3cos2t(sint)
(dxdt)=3sin2t(cost)
ds=9cos4tsin2t+9sin4tcos2t dt
ds=3sintcost dtcos2t+sin2t dt
ds=3sintcost dt
S=0π23sintcost dt=32(sint)20π2=32

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