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\begin{center}
{\Large TEST 3

Math 106 - 3}
\end{center}
\vspace{.1in}
You have 50 minutes to complete the test.
If it says, ``no calculator'', make sure I can follow your work without 
a calculator.
Show all relevant work (or else no credit).  
Make your work legible, if I can't read it, I can't grade it.  
Every problem is worth 10 points.
(There are only 70 points possible).
\vspace{.1in}

Name \rule{5in}{.2pt}

\vspace{.2in}

{\Large Formulas}

\[
\begin{array}{|l|l|}
\hline
\mbox{Sum and Difference} & \mbox{Double Angle} \\
\sin(u \pm v) = \sin u \cos v \pm \cos u \sin v & \sin 2u = 2 \sin u \cos u \\
\cos(u \pm v) = \cos u \cos v \mp \sin u \sin v & \cos su = \cos^2 u - \sin^2 u \\
\hline
\mbox{Power-Reducing} & \mbox{Half-Angle} \\
\sin^2 u = \frac{1-\cos 2u}{2} & \sin \frac{u}{2} = \pm \sqrt{\frac{1-\cos u}{2}} \\
\cos^2 u = \frac{1+\cos 2u}{2} & \cos \frac{u}{2} = \pm \sqrt{\frac{1+\cos u}{2}} \\
\hline
\mbox{Product to Sum} & \mbox{Sum to Product} \\
\sin u \sin v = \frac{1}{2} [ \cos(u-v) - \cos(u+v)] & 
	\sin x + \sin y = 2 \sin \left( \frac{x+y}{2} \right) 
		\cos \left( \frac{x-y}{2} \right) \\
\cos u \cos u = \frac{1}{2} [ \cos(u-v) + \cos(u+v)] &
	\cos x + \cos y = 2 \cos \left( \frac{x+y}{2} \right) 
		\cos \left( \frac{x-y}{2} \right) \\
\sin u \cos v = \frac{1}{2} [ \sin(u+v) + \sin(u-v)] & \\
\hline
\end{array}
\]

\begin{enumerate}

\item  Evaluate without a calculator
\[
\sin^{-1} \left( \frac{\sqrt{3}}{2} \right)
\]
\vspace{1.4in}

\item Write an algebraic expression equivalent to the given expression, for
$ -2 \leq x \leq 0$. (Your answer should have no $\sin$ or $\cos$ in it.)
\[
\cos( \arcsin (\frac{x}{2}))
\]
%\vspace{3in}
\newpage

\item Verify the identity
\[
\cos x(\tan^2 x +1) = \sec x
\]
\vspace{3.5in}

\item  Solve the equation without a calculator
\[
2\cos^2 3x + \cos 3x = 0
\]
%\vspace{3in}
\newpage

\item  Find the exact value without a calculator
\[
\sin \left( \frac{17 \pi}{12} \right)
\]
\vspace{2.5in}

\item  Given that $\cos x = -\frac{1}{9}$ and $\pi \leq x \leq \frac{3\pi}{2}$.
Find $\sin 2x$.
\vspace{3.2in}

\item  Find the exact value of $\cos 195^{\circ} + \cos 105^{\circ}$.
(You may do this any way you want, but one of the formulas should make it easier).

\end{enumerate}


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