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\centerline{\textbf{\large Exam \#1 $\cdot$ Wednesday September 27, 2006}}
\vspace*{.2in}
MATH 111 $\cdot$ Section 7 $\cdot$ Fall 2006  \hspace*{0.5in} Name \hrulefill
\vspace*{0.2in}

%%% ----------------------------------------------------------------
%\textbf{Problem 1.} (This is a writing problem.  Please use complete
%sentences.) Must all equilateral triangles be similar?  Explain.
%\vspace*{2.0in}

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\textbf{Problem 1.} (This is a writing problem.  Please use complete
sentences.) Is it possible for $\sin\theta$, $\cos\theta$, and $\tan\theta$
to all be negative for the same value of $\theta$?  Explain.
\vspace*{2.0in}

%%% ----------------------------------------------------------------
%\textbf{Problem 1.} Match each term to its definition.  (Some definitions
%will not be used.)
%\vspace*{0.1in}
%
%\begin{tabular}{lll}
%	\textbf{Term} &
%	$\qquad\qquad\qquad$
%	\textbf{Definition} & \\
%%
%	\_\_\_\_\_\_\_\_ \emph{a}. Acute angle &
%	$\qquad\qquad\qquad$
%	(\emph{i}) a shift to the right by $4$ \\
%%
%	\_\_\_\_\_\_\_\_ \emph{b}. Isosceles triangle &
%	$\qquad\qquad\qquad$
%	(\emph{ii}) a vertical expansion by a factor of 4 \\
%%
%	\_\_\_\_\_\_\_\_ \emph{c}. Supplementary angles &
%	$\qquad\qquad\qquad$
%	(\emph{iii}) a reflection about the $x$-axis \\
%%
%	\_\_\_\_\_\_\_\_ \emph{d}. Similar angles &
%	$\qquad\qquad\qquad$
%	(\emph{iv}) a horizontal expansion by a factor of 4 \\
%%
%	\_\_\_\_\_\_\_\_ \emph{e}. Coterminal angles &
%	$\qquad\qquad\qquad$
%	(\emph{v}) a shift up by 4 \\
%%
%	\_\_\_\_\_\_\_\_ \emph{f}. Obtuse triangle &
%	$\qquad\qquad\qquad$
%	(\emph{vi}) a vertical compression by a factor of 1/4 \\
%%
%	& $\qquad\qquad\qquad$
%	(\emph{vii}) a reflection about the $y$-axis \\
%%
%	& $\qquad\qquad\qquad$
%	(\emph{viii}) a shift to the left by $4$ \\
%\end{tabular}
%\vspace*{0.1in}

%%% ----------------------------------------------------------------
%\textbf{Problem 2.} Two supplementary angles have measure $(3m+2)^\circ$ and
%$(5m+6)^\circ$.  Find the numerical values of their measures, in degrees.
%\vspace*{1.0in}

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\textbf{Problem 3.}  Solve for $x$:  $\sin(3x+2^\circ) = \cos(8x)$.
(Hint:  use a cofunction identity.)
\vspace*{1.0in}
%\newpage

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\textbf{Problem 4.} Consider the following figure:
\vspace*{1.2in}

\textbf{Part (a)} What trigonometric function of $\theta$ does $m/z$ represent?
\vspace*{1.0in}

\textbf{Part (b)} What trigonometric function of $\theta$ does $z/a$ represent?
%\vspace*{1.0in}
\newpage

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\textbf{Problem 5.} Let $\theta=-135^\circ$.
\vspace*{0.1in}

\textbf{Part (a)} Sketch $\theta$ in standard position.
\vspace*{1.0in}

\textbf{Part (b)} Find a positive and a negative angle (different from
$\theta$) which is coterminal with $\theta$.
\vspace*{1.0in}

\textbf{Part (c)} Write an algebraic expression for all angles which
are coterminal with $\theta$.
\vspace*{1.0in}

\textbf{Part (d)} Find $\cos(\theta)$ exactly.
\vspace*{1.0in}

%% ----------------------------------------------------------------
\textbf{Problem 6.}  True or false:
\vspace*{0.1in}

\textbf{Part (a)} It is possible for $\sin(\theta)=\sqrt 6$ for
some angle $\theta$.
\vspace*{1.0in}

\textbf{Part (b)} It is possible for $\sec(\theta)=0.8$ for
some angle $\theta$.
\vspace*{1.0in}

\textbf{Part (c)} It is possible for $\tan(\theta)=98.23$ for
some angle $\theta$.
%\vspace*{1.0in}
\newpage

%% ----------------------------------------------------------------
\textbf{Problem 7.}  The blueprint for a radio transmitter shows a tower 19.8
in tall with a cable running from the top of the tower to a point a point on
the ground 11.1 in to the left.  You approach the tower itself (not the
blueprint) and measure the distance from the base of the cable to the base of
the tower to be 347.9 ft.
\vspace*{1.4in}

\textbf{Part (a)} How tall is the tower?
\vspace*{1.0in}

\textbf{Part (b)} How long is the cable (assuming, for the sake of Math 111,
that it does not sag under its own weight)?
\vspace*{1.0in}

%% ----------------------------------------------------------------
\textbf{Problem 8.}  If a point $(a,b)$ is in quadrant III, what quadrant
is $(-a,b)$ in?
\vspace*{1.0in}

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\textbf{Problem 9.}  Find the measures of the angles $\alpha$ and $\beta$ and
the measures of the sides $m$, $n$, $p$, and $q$.
%\vspace*{1.2in}
\newpage

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\textbf{Problem 10.}  Which of the following is true for all angles $\theta$?

\begin{tabular}{lll}
(A) If $\sin(\theta) < 0$ then $\tan(\theta) < 0$. \\
(B) If $\tan(\theta) = 1/2$ then $\sin(\theta)=1$ and $\cos(\theta)=2$. \\
(C) $\sin(\theta) \ne \cos(\theta)$. \\
(D) If $\sin(\theta) < 0$ then $\csc(\theta) < 0$. \\
(E) None of these \\
\end{tabular}
\vspace*{1.0in}

%% ----------------------------------------------------------------
\textbf{Problem 11.}  An aircraft is flying over level ground.  (The direction
of flight is out of the page in the figure.) The plane's altimeter shows an
altitude of 2438 meters.  The pilot sees a target out the right window, and
measures that the target lies at an angle of $67.29^\circ$ from the vertical.
\vspace*{2.0in}

\textbf{Part (a)} In the previous paragraph, two numbers are mentioned.
Write them where they belong in the figure.
\vspace*{0.1in}

\textbf{Part (b)} What is the distance from the aircraft to the target?
\vspace*{2.0in}

%% ----------------------------------------------------------------
\textbf{Problem 12.}  Is $\cos(2\pi/3)$ greater than, equal to, or less than
$\cos(135^\circ)$?  Please explain your answer.
%\vspace*{1.0in}
\newpage

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\textbf{Problem 13.}  Find the surface area, in square feet, of the following
baseball field.  (Treat the outfield fence, i.e. the curved portion of the
perimeter of the field, as an arc of a circle.)
\vspace*{3.0in}
%\newpage

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\textbf{Problem 14.}  In the figure, how many times does the large gear
rotate counterclockwise for each time the smaller gear rotates one full
revolution clockwise?
\vspace*{1.0in}

%%% ----------------------------------------------------------------
%\textbf{Problem 2.} Which of the following graphs show $y$ as a function of $x$?
%\vspace*{0.1in}
%%\input{grfpapb123.tex}
%
%\begin{tabular}{lll}
%(A) II only \qquad\qquad&
%(B) I and II only \qquad\qquad &
%(C) I and III only \\
%(D) All of them  \qquad\qquad &
%(E) None of them \\
%\end{tabular}
%\vspace*{0.5in}

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\end{document}
