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Problems PreCal 1508 PLTL Workshop, October 19, 2011\\
PLs: Alex Knaust, Edith Mejia. Lecturer: Yi-Yu Liao\\

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Please do the problems that you feel will help your group the most first (you don't have to do them in order). All handouts are available at \url{http://alex.knaust.info/pltlfall2011/}

\begin{enumerate}
\item Draw and label the unit circle. (Without copying a sheet)

\item Find the complement and supplement of the following angles
\begin{enumerate}
\item $\frac{\pi}{4}$
\item $1.5$
\item $\frac{\pi}{12}$
\end{enumerate}

\item Convert from degrees to radians
\begin{enumerate}
\item 45\degree
\item 123\degree
\item -99\degree
\end{enumerate}

\item Find the length of the arc of a circle for the following radii and angles
\begin{enumerate}
\item $\theta = \frac{\pi}{4}, \quad r = 2$
\item $\theta = 29\degree, \quad r = 5$
\item $\theta = \frac{7\pi}{5}, \quad r = 1$
\end{enumerate}

\item I travelled at constant speed for 5 meters in 23 seconds on my unicycle. I know my cycle's tire has an .875 meter diameter. How many revolutions per second did the wheel travel at?

\item Find the following values
\begin{enumerate}
\item $\sin \left(\frac{\pi}{4}\right)$
\item $\cot \left(\frac{\pi}{3}\right)$
\item $\cos \left(\frac{7\pi}{6}\right)$
\item $\tan \left(30\degree\right)$
\end{enumerate}

\item My peer leader told me that $\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$ and my teacher told me that $\tan(x) = \frac{\sin(x)}{\cos(x)}$. Which one is right? Explain. 

\item Do the following lengths (side, side, hypotenuse) represent valid right triangles?
\begin{enumerate}
\item $3, \sqrt{3}, 2$ 
\item $3, 4, 5$
\item $\sqrt{2}, \sqrt{2}, 2$
\end{enumerate}
\item Given you know only that $\sin$ and $\cos$ are odd and even functions respectively, show that $\tan$ is an odd function.
\end{enumerate}
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