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\large{
\centerline{Math 1321 Sec. 17, Sample Test \# 3,\ \ Name
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\begin{enumerate}
\item Use a half angle formula to find the exact value of $\dst
\sin\left(\frac{\pi}{8}\right)$

\vspace{.15in}

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\item Solve $2\sin(\ta)\cos(\ta )-4\sin(\ta)-\cos(\ta)+2=0$ for  $\ta$ on the interval
$0\leq \ta<2\pi$. 

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\item Sketch the graph of \ $\dst y=5\sin\left(\frac{\ta}{2}+\frac{\pi}{4}\right)$ on
$(-\pi/2,7\pi/2)$ and find the amplitude, period and phase shift. 

\parbox{3in}{\begin{picture}(150,100)(0,0)
\put(1,50) {\vector(1,0){150}} 
\put(15,1) {\vector(0,1){100}}         
\end{picture}}

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\item Express $y=\sqrt{3}\sin(\ta)-\cos(\ta)$ in the form $y=a\sin(b\ta +c)$

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\item Find $\sin \big(\text{Tan}^{-1}u\big)$.
\vspace{.15in}

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\item \parbox[t]{3.5in}{In the following right triangle\\ $b=166$ and $A=56.1^\circ$, find
$c$.}
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\parbox{2.5in}{\includegraphics[scale=.7]{rt_triangle.epsf}}

\vspace{.15in}

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\item Compute the exact value of \ \ \  
$\dst 20\sin^4(45^\circ)-6\cos^2(30^\circ)+3\sin^3(30^\circ)-\sin(0^\circ)$\\
(No Calculators -  show work with exact answers at each
step) 
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\item San Bernadino, Calif., is $100$ miles due north of San Diego. Yuma, Ariz. is
\textit{S} $56^\circ$\textit{E} from San Bernadino and due east of San Diego. How far is
Yuma from San Bernadino?

\end{enumerate}
}
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