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\problemgrouptitle{Polar Coordinates}

\addtoanswerkey{\begin{multicols}{2}}

\begin{problemblock}[2]{Find Cartesian coordinates of the given point.}

\item $\displaystyle(r,\theta)=\left(2,\frac{\pi}{3}\right)$
\answer{
$(x,y)=\left(1,\sqrt{3}\right)$
}

\item $\displaystyle(r,\theta)=\left(3,\frac{3\pi}{2}\right)$
\answer{
$(x,y)=\left(0,-3\right)$
}

\item $\displaystyle(r,\theta)=\left(4,\frac{5\pi}{4}\right)$
\answer{
$(x,y)=\left(-2\sqrt{2},-2\sqrt{2}\right)$
}

\item $\displaystyle(r,\theta)=\left(1,\frac{5\pi}{6}\right)$
\answer{
$(x,y)=\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)$
}

\end{problemblock}

\begin{problemblock}[2]{Find polar coordinates of the given point.}

\item $\displaystyle(x,y)=\left(1,-1\right)$
\answer{
$(r,\theta)=\left(\sqrt{2},\frac{7\pi}{4}\right)$
}

\item $\displaystyle(x,y)=\left(2\sqrt{3},2\right)$
\answer{
$(r,\theta)=\left(4,\frac{\pi}{6}\right)$
}

\item $\displaystyle(x,y)=\left(-5,0\right)$
\answer{
$(r,\theta)=\left(5,\pi\right)$
}

\item $\displaystyle(x,y)=\left(-4,-4\sqrt{3}\right)$
\answer{
$(r,\theta)=\left(8,\frac{4\pi}{3}\right)$
}

\end{problemblock}

\addtoanswerkey{\end{multicols}}

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