# 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 .
Calculate the arc length of $\frac{1}{4}$ of the astroid $\left(0\le t\le \frac{\pi }{2}\right)$
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## Expert Answer

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

$ds=\sqrt{{\left(\frac{dx}{dt}\right)}^{2}+{\left(\frac{dy}{dt}\right)}^{2}}$
$\left(\frac{dx}{dt}\right)=3{\mathrm{cos}}^{2}t\left(-\mathrm{sin}t\right)$
$\left(\frac{dx}{dt}\right)=3{\mathrm{sin}}^{2}t\left(\mathrm{cos}t\right)$

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