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\def\header{{\hfill Exam 3 \hfill A. Miller \hfill Spring 2001
                                       \hfill Math 217\hfill}}
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\probno=0
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       \string& #1 \string&
       \string\qquad \string\\ \string\hline}}

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       \string& #1 \string&
       \string\qquad \string\\ \string\hline}}

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    \immediate\write\examTBLFile{Total \string& \the\total
    \string& \qquad \string\\ \string\hline}
     }

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\immediate\openout\ans=answers
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\def\printanswers{\newpage\begin{center} Answers \end{center}
    \immediate\closeout\ans\input answers}

\begin{document}

\bigskip

Show all work. {\bf Circle your answer.}

No books, no notes, no calculator, no cell phones, no pagers, no
electronic devices at all.

Solutions will be posted shortly after the exam:
www.math.wisc.edu/$\sim$miller/m217

\par\vskip .25in
\begin{center}
Name\makebox[3in]{\hrulefill} \\
\end{center}

\begin{center}
{\bf Hand in to your TA -- Circle your DIScussion section (column one):} \\
\end{center}
\begin{center}
\begin{tabular}{l|l|l|l}
DIS 321 & 7:45   TR  & 901  Van Vleck & Forray, Susan Jane     \\
DIS 322 & 8:50   TR  & 6224 Soc Sci   & Bisgard, James William \\
DIS 324 & 9:55   TR  & 123  Ingraham  & Bisgard, James William \\
DIS 326 & 11:00  TR  & B235 Van Vleck & Leete, Jennifer A.     \\
DIS 327 & 11:00  TR  & 113  Ingraham  & Lu, Tianshi            \\
DIS 328 & 12:05p TR  & B235 Van Vleck & Leete, Jennifer A.     \\
DIS 329 & 12:05p TR  & 6228 Soc Sci   & Lu, Tianshi            \\
DIS 330 & 1:20p  TR  & B321 Van Vleck & Forray, Susan Jane     \\
DIS 332 & 2:25p  TR  & B135 Van Vleck & Hur, Youngmi           \\
DIS 334 & 3:30p  TR  & B329 Van Vleck & Hur, Youngmi           \\
\end{tabular}
\end{center}





% end file with \finishtbl
%\bigskip

\begin{center} \Large
 \begin{tabular}{||c|c|c||} \hline\hline
  Problem & Points & Score \\  \hline\hline
  \input{exam.tbl}
  \hline \hline
 \end{tabular}
\end{center}

\immediate\openout\examTBLFile=exam.tbl

\setcounter{page}{0}

\def\deg{\circ}

\prob{10} % 7.2-7
Find the value of
$$\cos(12^\deg)\cos(-18^\deg)\;+\; \sin(18^\deg)\sin(-12^\deg)$$
and simplify it.
\answer $\cos(30^\deg)={\sqrt{3}\over 2}$

\prob{10} % 7.3-25
Find $\sin^2({\theta\over 2})$ given that $\cos(\theta)={{4\over 5}}$.
\answer $1\over 10$

\prob{10} % 7.5-27
Find  all $\theta$ which solve the equation:
$$2\sin(\theta)\cos(\theta)\;+\;2\sin(\theta)\;+\;\cos(\theta)\;+\;1=0$$
\answer \par
\par $\theta=\pi + 2\pi n$ or
\par $\theta=-{\pi\over 6}+2\pi n$ or
\par $\theta=-{5\pi\over 6}+2\pi n$
\par for $n=0,1,-1,2,-2,\ldots$.

\prob{10} % 6.1
Suppose $z=\tan(\theta)\sec(\theta)$.
\par\medskip Find $dz\over d\theta$.
\par\medskip Simplify and express in terms of $\sec(\theta)$ only.
\par\medskip \answer $2\sec^3(\theta)-\sec(\theta)$

\prob{10} % 6.3
Find the value of
$$\int_0^2 {dx\over{1+{x^2\over 4}}}$$
and simplify.
\answer $\pi\over 2$


\prob{10}
Prove Pythagorus's Theorem.  In a right triangle with
hypotenus $c$ and sides $a$ and $b$, we have that

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\put(68.00,10.00){\rule{2.00\unitlength}{2.00\unitlength}}
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\answerx After removing the triangles the remaining areas must be equal.
(I would have shaded the triangles but my computer program wasn't up
to it.)
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\begin{picture}(110.00,53.00)
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\put(10.00,20.00){\line(1,3){10.00}}
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\put(95.00,53.00){\makebox(0,0)[cc]{$b$}}
\put(67.00,25.00){\makebox(0,0)[cc]{$b$}}
\put(33.00,41.00){\makebox(0,0)[cc]{$c$}}
\end{picture}



\finishtbl
\printanswers

\end{document}