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Problems PreCal 1508 PLTL Workshop, November 11, 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 Determine the domain and range of the trigonometric functions, and the (restricted) domain and ranges of their inverse functions.

\item Sketch a graph of $\sin^{-1}$, $\cos^{-1}$ and $\tan^{-1}$.

\item Evaluate the following expressions with inverse functions without the use of a calculator
\begin{enumerate}
\item $\arctan(-\sqrt{3})$
\item $\cos^{-1}(1)$
\item $\arcsin \left(-\frac{\sqrt{2}}{2}\right)$
\end{enumerate}


\item Use the properties of inverse functions to find the following values (Sketching a right triangle may help)
\begin{enumerate}
\item $\sin\left(\arcsin\left(\frac{1}{2}\right)\right)$
\item $\sin\left(\arctan\left(\frac{3}{4}\right)\right)$
\item $\cot\left( \arctan \left(\frac{5}{8}\right)\right)$
\end{enumerate}

\item Graph $f(x) = \tan(3x - 2) + 1$

\item Solve for $x$ in the following equation 
 \[2\cos x + 1 = 0 \]
\item A periodic function, $f$, with period $t$ has the property that for any $x$ in the domain of $f$. 
	\[f(x + t) = f(x)\]
\begin{enumerate}
\item You know that trigonometric functions are periodic, So is
 $\sin(x + \pi) = \sin(x - \pi)$ true?
 
\item Can periodic functions have inverses?
\item Do periodic functions always have inverses in one cycle of the period?
\item Can you think of a periodic function that isn't trigonometric?
\end{enumerate}

\end{enumerate}
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