<s>[INST] Find equation of a circle given a sector A sector of a semi-circle which is $60^\circ$ has an area of $\frac{3\pi}{2}$ units squared.
Show that the curved section is a function of the form $f(x)= \sqrt{9-x^2}$ with domain $[0,\frac{3\sqrt{3}}{2}]$
 [/INST] Area of sector
\begin{align}
A&=\frac{60^\circ}{360^\circ}\pi r^2\\
\frac{3\pi}{2}&=\frac{1}{6}\pi r^2\\
r&=3
\end{align}
Equation of circle with center on the origin
\begin{align}
x^2+y^2&=r^2\\
x^2+y^2&=3^2\\
y&=\sqrt{9-x^2}
\end{align}
then use parametric equation (polar coordinate) $x=r\cos\theta$ and $y=r\sin\theta$ to determine the domain.
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