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\begin{center}
{\Large TEST 3

Math 142}
\end{center}

\begin{itemize}
\item  Do your work on separate paper.  Show all your work and make your work neat.  
	You will be graded on both your answer and (most importantly) your work.
\item  You can use a calculator and one $3 \times 5$ not card of notes.
\item  4 problems worth 10 points each.
\end{itemize}



\begin{enumerate}


\item	\[
	r = 2\cos\theta
	\]
	\begin{enumerate}
	\item  Graph the polar equation.
		Graph it by hand (without your calculator).
	\item  Convert the polar equation to an equation in rectangular coordinates.
	\end{enumerate}


\item  
	\begin{enumerate}
	\item  Graph the complex number $-4\sqrt{2}+4\sqrt{2}\;i$.
	\item  Find the trigonometric form of the complex number $-4\sqrt{2}+4\sqrt{2}\;i$.
		(It might help to convert the angle to degrees to check and make sure your angle is in the right quadrant.)
	\item  Find all cube roots of $-4\sqrt{2}+4\sqrt{2}\;i$.
		Write your answers in both trigonometric form and standard form.
	\end{enumerate}


\newpage

\item  In repairing your roof, you need to determine the angles of your roof.
	You make the measurements as in the drawing.
	What are the angles?
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\item  You are standing at point $A$ below and you can see point $B$ and $C$ in this distance.
	You measure the angle from point $B$ and $C$ to be $50^\circ$.
	You also know that the distance from you to point $B$ is $5$ miles and the distance from point $B$ to point $C$ is $4$ miles.
	How far are you from point $C$?
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\end{enumerate}

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