<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\newcommand{\ds}{\displaystyle}
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{\bf Question}

Express the following curves in cylindrical polar coordinates:
\begin{description}
\item[(a)] $x^2 + y^2 = 1$
\item[(b)] $x^2 + y^2 + z^2 = 1$
\item[(c)]$(x - \frac{1}{2})^2 + y^2  =  1 $
\item[(d)] $y = x\tan \phi_0$, where $\phi_0$ is a constant.
\end{description}

\vspace{.25in}

{\bf Answer}

\begin{description}
\item[(a)] $r^2 = 1$
\item[(b)] $r^2 + z^2 = 1$
\item[(c)]$(r \cos \phi - \frac{1}{2})^2 + r^2 \sin ^2
\phi  =  1 $

$ r^2 \cos^2 \phi - 2r \cos \phi + \frac{1}{4} + r^2 \sin^2 \phi =
 1 $

$ r^2 - r \cos \phi - \frac{3}{4}  =  0$
\item[(d)] $\frac{y}{x} = \tan \theta = \tan \phi_0$ therefore
$\theta = \phi_0$
\end{description}


\end{document}
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