%
% file:         trig/quizzes.tex
% created:      pasha sep 5-6,10 2013
% modified:     pasha sep 12,26 2013
% modification: 
%

\documentclass[12pt,a4paper]{amsart}
\hoffset=-2cm \voffset=-2cm \topmargin=10pt \textheight=25.5cm \textwidth=16.6cm 
\pagestyle{plain}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\theoremstyle{remark}
\newtheorem*{question}{Question}

% to force enumeration with roman numbers
\renewcommand{\labelenumi}{(\roman{enumi})}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\renewcommand{\sectionname}{Quiz}


\begin{document}

\title{Quizzes for 1020 College Algebra and Trigonometry}
\author{Pasha Zusmanovich}
\address{}
\email{pzusmanovich@nccu.edu}
\date{\today}

\maketitle


\section{} % 1

Draw an angle of $1$ radian. Is this angle: acute, right, obtuse, straight?



\section{} % 2

What is bigger: $\sin 45^o$ or $\cos \frac{\pi}4$ ?




\section{} % 3

A wheel rotates with an angular speed $1$ rad/sec. How many rotations it makes 
in $1$ minute?



\section{} % 4

Is the following equality true: 
$\sin^2 \frac{\pi}3  + \cos^2 \frac{\pi}3 = 
 \sin^2 \frac{2\pi}3 + \cos^2 (-\frac{2\pi}3)$ ?




\section{} % 5

Can the same function be both even and odd?



\section{} % 6

Which of the following inequalities is true for all positive numbers $x$:
\begin{enumerate}
\item $2 \sin(x) \ge \sin(x)$ ;
\item $\sin(2x) \ge \sin(x)$ ?
\end{enumerate}



\section{} % 7

Draw a graph of the function $y = 2 \sin (x - \frac{\pi}2)$.


\section{} % 8

\begin{enumerate}
\item Find $x$ such that $cos^{-1}(x) = 0$.
\item Find the exact value of $sin^{-1}(-2)$.
\end{enumerate}


\section{} % 9

Verify the identity: 
$$
\frac{cos(-x)}{sin(-x)} = - \frac{1}{tan(x)} .
$$




\end{document}
%eof

