\documentclass[11 pt, a4paper, fleqn]{article} % fleqn aligns equations left
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\setlength{\textheight}{24 cm} % height of actual text
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% In practice this seems to give equal margins with just about the right text width.
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\usepackage{times} % nice text fonts
\usepackage{multicol}
%\usepackage{amsmath} % easier equation alignment etc
%\usepackage{amsfonts} % to get extra symbols
%\usepackage{graphicx} if you want to include *.eps pictures
% USE \begin{quest} ... \end{quest} for main questions list.
% USE \begin{subq}... \end{subq} for alphabetically listed subquestions.
\begin{document}
\section*{S6 PURE MATHEMATICS \hfill 2-2-99} % \hfill gets date right aligned
\bfseries Trigonometry  \hfill \underline{Show all working clearly}

\normalfont
\newcommand{\marks}[1]{\marginpar{\hfill {\bfseries \small{#1}}}} %defining marks command
\newcounter{qno}% if we don't declare the counter it won't work.
\newenvironment{quest} % main question list environment
{
\begin{list}{\arabic{qno})}
{
\usecounter {qno}
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}
{\end{list}
} % end of definition
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}
}
{\end{list}
} % end of definition
\begin{quest}
\vspace{-0.2 cm}
\item In each case express the trigonometrical ratio in terms of an acute angle.\\
(Examples: \(\sin 200^\circ=-\sin 20^\circ\), \quad \(\cos 300^\circ=\cos 60^\circ.\)) 
\begin{multicols}{4}
\begin{subq}
\item \(\sin 250^\circ\)
\item \(\cos 250^\circ\)
\item \(\tan 250^\circ\)
\item \(\sin 132^\circ\)
\item \(\cos 132^\circ\)
\item \(\tan 132^\circ\)
\item \(\sin (-75^\circ)\)
\item \(\cos (-75^\circ)\)
\item \(\tan (-75^\circ)\)
\item \(\sin 346^\circ\)
\item \(\cos 346^\circ\)
\item \(\tan 346^\circ\)
\end{subq}
\end{multicols}
\marks{[24]}
\item Express the following angles in radians:
\begin{subq}
\begin{multicols}{4}
\item \(300^\circ\)
\item \(60^\circ\)
\item \(120^\circ\)
\item \(315^\circ\)
\item \(225^\circ\)
\item \(30^\circ\)
\item \(600^\circ\)
\item \(15^\circ\)
\item \(330^\circ\)
\item \(720^\circ\)
\item \(135^\circ\)
\item \(270^\circ\)
\end{multicols}
\end{subq}
\marks{[12]}

\item Express the following angles in degrees:
\begin{subq}
\begin{multicols}{4}
\item \(2 \pi\)
\item \(\frac{\pi}{4}\)
\item \(\frac{3 \pi}{4}\)
\item \(\frac{5 \pi}{6}\)
\item \(\frac{7 \pi}{6}\)
\item \(\frac{5 \pi}{3}\)
\item \(\frac{5 \pi}{4}\)
\item \(\frac{3 \pi}{2}\)
\item \(\frac{2 \pi}{3}\)
\item \(\frac{5 \pi}{3}\)
\item \(\frac{2 \pi}{9}\)
\item \(\frac{\pi}{12}\)
\end{multicols}
\end{subq}
\marks{[12]}



\item Find all solutions between \(0^\circ\) and \(360^\circ\) of the following equations:
\begin{multicols}{4}
\begin{subq}
\item \(\sin \theta = \frac{1}{2}\)
\item \(\sin \theta = 0\)
\item \(\cos \theta = -\frac{1}{2}\)
\item \(\tan \theta = \sqrt{3}\)
\item \(\sin 2\theta = -\frac {1}{\sqrt{2}}\)
\item \(\cos 3\theta = 0\)
\item \(\sin^2\theta = \frac{3}{4}\)
\item \(\tan \theta = 1\)
\item \(\tan 2\theta = -\sqrt{3}\)
\item \(\sin \theta = -1\)
\item \(\sin 5\theta = \frac{1}{2}\)
\item \(\cos 5\theta = -1\)
\end{subq}
\end{multicols}
\marks{[24]}
\item Draw neat, clearly labelled sketch graphs of the following for \(0^\circ \leq x \leq 360^\circ\) :
\begin{subq}
\item \(y=\cos 2x\)
\item \(y=5+\sin x\)
\item \(y=\sin(x-45^\circ)\)
\item \(y=1+\cos 3x\)
\end{subq}
\marks{[12]}
\item 
\begin{subq}
\item Make a table of values and draw an accurate graph of \(y=\sin^2 x\).
\item Draw a clear labelled sketch of the graph of \(y=1-\cos 2x\).
\item Draw an intellegent conclusion.
\end{subq}
\marks{[12]}
\item Prove that for all angles \(\theta\), \(\sin^2 \theta + \cos^2 \theta = 1\). \marks{[4]}
\item Given that \(\cos \phi = \frac {5}{13}\) and \(\phi\) is acute, find the exact values of \(\sin \phi\) and \(\tan \phi\).  \marks{[4]}
\item Given that \(\sin \psi = \frac {2}{7}\) and \(\psi\) is obtuse, find, as surds the values of \(\cos \psi\) and \(\tan \psi\). \marks{[4]}








\end{quest}
\end{document}
