代表的な角度の三角比 - 数式で独楽する

代表的な角度の三角比をまとめます。

\begin{array}{ccccc}
\hline
\displaystyle \frac{\theta}{\mathrm{deg}} & \displaystyle \frac{\theta}{\mathrm{rad}} & \sin \theta & \cos \theta & \tan \theta \\ \hline
0 & 0 & 0 & 1 & 0 \\
15 & \displaystyle \frac{\pi}{12} & \displaystyle \frac{\sqrt{6}-\sqrt{2}}{4} & \displaystyle \frac{\sqrt{6}+\sqrt{2}}{4} & 2-\sqrt{3} \\
18 & \displaystyle \frac{\pi}{10} & \displaystyle \frac{\sqrt{5}-1}{4} & \displaystyle \frac{\sqrt{10+2\sqrt{5} \ }}{4} & \displaystyle \frac{\sqrt{25-10\sqrt{5} \ }}{5} \\
22.5 & \displaystyle \frac{\pi}{8} & \displaystyle \frac{\sqrt{2-\sqrt{2} \ }}{2} & \displaystyle \frac{\sqrt{2+\sqrt{2} \ }}{2} & \sqrt{2}-1 \\
30 & \displaystyle \frac{\pi}{6} & \displaystyle \frac{1}{2} & \displaystyle \frac{\sqrt{3}}{2} &
\displaystyle \frac{1}{\sqrt{3}} \\
36 & \displaystyle \frac{\pi}{5} & \displaystyle \frac{\sqrt{10-2\sqrt{5} \ }}{4} & \displaystyle \frac{\sqrt{5}+1}{4} & \sqrt{5-2\sqrt{5} \ } \\
45 & \displaystyle \frac{\pi}{4} & \displaystyle \frac{1}{\sqrt{2}} & \displaystyle \frac{1}{\sqrt{2}} & 1 & \\
54 & \displaystyle \frac{3}{10} \pi & \displaystyle \frac{\sqrt{5}+1}{4} & \displaystyle \frac{\sqrt{10-2\sqrt{5} \ }}{4} & \displaystyle \frac{\sqrt{25+10\sqrt{5} \ }}{5} \\
60 & \displaystyle \frac{\pi}{3} & \displaystyle \frac{\sqrt{3}}{2} & \displaystyle \frac{1}{2} &
\sqrt{3} \\
67.5 & \displaystyle \frac{3}{8} \pi & \displaystyle \frac{\sqrt{2+\sqrt{2} \ }}{2} & \displaystyle \frac{\sqrt{2-\sqrt{2} \ }}{2} & \sqrt{2}+1 \\
72 & \displaystyle \frac{2}{5} \pi & \displaystyle \frac{\sqrt{10+2\sqrt{5} \ }}{4} & \displaystyle \frac{\sqrt{5}-1}{4} & \sqrt{5+2\sqrt{5} \ } \\
75 & \displaystyle \frac{5}{12} \pi & \displaystyle \frac{\sqrt{6}+\sqrt{2}}{4} & \displaystyle \frac{\sqrt{6}-\sqrt{2}}{4} & 2+\sqrt{3} \\
90 & \displaystyle \frac{\pi}{2} & 1 & 0 & \infty \\
\hline
\end{array}