basic-trig.tex

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\[
\arraycolsep=1.5em\def\arraystretch{3}
\begin{array}{cc}
%%
\arraycolsep=0.5em
\begin{gathered}[t]\textbf{Important Angles}\\
\begin{array}{c|ccc}
        \theta  & \sin\theta          & \cos\theta          & \tan\theta         \\
\hline
            0   &             {0}     &             {1}     &             {0}     \\
\dfrac{\pi}{6}  & \dfrac      {1} {2} & \dfrac{\sqrt{3}}{2} & \dfrac{\sqrt{3}}{3} \\
\dfrac{\pi}{4}  & \dfrac{\sqrt{2}}{2} & \dfrac{\sqrt{2}}{2} &             {1}     \\
\dfrac{\pi}{3}  & \dfrac{\sqrt{3}}{2} & \dfrac      {1} {2} &        \sqrt{3}     \\
\dfrac{\pi}{2}  &             {1}     &             {0}     &       \infty
\end{array}\end{gathered}
&
\begin{gathered}[t]
%%%%%%%%%%%%%%%%
\begin{gathered}[t]\textbf{Fundamental Identities}\\
\begin{aligned}
\sin^2\theta+\cos^2\theta&=1\\[.5em]
\sec^2\theta-\tan^2\theta&=1\\[.5em]
\csc^2\theta-\cot^2\theta&=1
\end{aligned}\end{gathered}
\\[3em]
\begin{gathered}[t]\textbf{Half-Angle Formulae}\\
\begin{aligned}
\cos^2x=\frac{1+\cos{2\theta}}{2}\\[1em]
\sin^2x=\frac{1-\cos{2\theta}}{2}
\end{aligned}\end{gathered}
\\[3em]
\begin{gathered}[t]\textbf{Double-Angle Formulae}\\
\begin{aligned}
  \cos{2x}&=\cos^2x-\sin^2x\\&=2\cos^2x-1\\&=1-2\sin^2x\\[0.5em]
  \sin{2x}&=2\sin x \cos x\\[0.5em]
  \tan{2x}&=\frac{2\tan x}{1-\tan x}
\end{aligned}\end{gathered}
%%%%%%%%%%%%%%
\end{gathered}
\end{array}
\]







\endgroup