３°刻みの三角比の値
値の求め方は、PDF にあります。
３°刻みの三角比
\(
\\
\begin{cases}
\sin0°=0 \\
\cos0°=1
\end{cases}
\\
\begin{cases}
\sin3°=\displaystyle\frac{\sqrt{2}(\sqrt{3}+1)(\sqrt{5}-1)-2(\sqrt{3}-1) \sqrt{\sqrt{5}+5}}{16} \\
\cos3°=\displaystyle\frac{\sqrt{2}(\sqrt{3}-1)(\sqrt{5}-1)+2(\sqrt{3}+1) \sqrt{\sqrt{5}+5}}{16}
\end{cases}
\\
\begin{cases}
\sin6°=\displaystyle\frac{\sqrt{2}\sqrt{3}(\sqrt{5}-1)\sqrt{\sqrt{5}+5}-2(\sqrt{5}+1)}{16} \\
\cos6°=\displaystyle\frac{\sqrt{2}(\sqrt{5}-1)\sqrt{\sqrt{5}+5}+2\sqrt{3}(\sqrt{5}+1)}{16}
\end{cases}
\\
\begin{cases}
\sin9°=\displaystyle\frac{\sqrt{2}(\sqrt{5}+1)-(\sqrt{5}-1)\sqrt{\sqrt{5}+5}}{8} \\
\cos9°=\displaystyle\frac{\sqrt{2}(\sqrt{5}+1)+(\sqrt{5}-1)\sqrt{\sqrt{5}+5}}{8}
\end{cases}
\\
\begin{cases}
\sin12°=\displaystyle\frac{\sqrt{2}\sqrt{\sqrt{5}+5}-\sqrt{3}(\sqrt{5}-1)}{8} \\
\cos12°=\displaystyle\frac{\sqrt{2}\sqrt{3}\sqrt{\sqrt{5}+5}+(\sqrt{5}-1)}{8}
\end{cases}
\\
\begin{cases}
\sin15°=\displaystyle\frac{\sqrt{2}(\sqrt{3}-1)}{4} \\
\cos15°=\displaystyle\frac{\sqrt{2}(\sqrt{3}+1)}{4}
\end{cases}
\\
\begin{cases}
\sin18°=\displaystyle\frac{ \sqrt{5}-1}{4} \\
\cos18°=\displaystyle\frac{ \sqrt{2}\sqrt{\sqrt{5}+5} }{4}
\end{cases}
\\
\begin{cases}
\sin21°=\displaystyle\frac{ (\sqrt{3}+1)(\sqrt{5}-1) \sqrt{\sqrt{5}+5}-\sqrt{2}(\sqrt{3}-1)(\sqrt{5}+1) }{16} \\
\cos21°=\displaystyle\frac{ (\sqrt{3}-1)(\sqrt{5}-1) \sqrt{\sqrt{5}+5}+\sqrt{2}(\sqrt{3}+1)(\sqrt{5}+1) }{16}
\end{cases}
\\
\begin{cases}
\sin24°=\displaystyle\frac{ 2\sqrt{3}(\sqrt{5}+1)-\sqrt{2}(\sqrt{5}-1)\sqrt{\sqrt{5}+5} }{16} \\
\cos24°=\displaystyle\frac{ 2(\sqrt{5}+1)+\sqrt{2}\sqrt{3}(\sqrt{5}-1)\sqrt{\sqrt{5}+5} }{16}
\end{cases}
\\
\begin{cases}
\sin27°=\displaystyle\frac{ 2\sqrt{\sqrt{5}+5}-\sqrt{2}(\sqrt{5}-1) }{8} \\
\cos27°=\displaystyle\frac{ 2\sqrt{\sqrt{5}+5}+\sqrt{2}(\sqrt{5}-1) }{8}
\end{cases}
\\
\begin{cases}
\sin30°=\displaystyle\frac{ 1 }{ 2 } \\
\cos30°=\displaystyle\frac{ \sqrt{ 3 } }{ 2 }
\end{cases}
\\
\begin{cases}
\sin33°=\displaystyle\frac{ 2(\sqrt{3}-1) \sqrt{\sqrt{5}+5} + \sqrt{2}(\sqrt{3}+1)(\sqrt{5}-1) }{16} \\
\cos33°=\displaystyle\frac{ 2(\sqrt{3}+1) \sqrt{\sqrt{5}+5} - \sqrt{2}(\sqrt{3}-1)(\sqrt{5}-1) }{16}
\end{cases}
\\
\begin{cases}
\sin36°=\displaystyle\frac{ \sqrt{2}( \sqrt{5}-1 )\sqrt{\sqrt{5}+5} }{8} \\
\cos36°=\displaystyle\frac{ \sqrt{5}+1}{4}
\end{cases}
\\
\begin{cases}
\sin39°=\displaystyle\frac{ \sqrt{2}( \sqrt{3}+1 )( \sqrt{5}+1 ) - ( \sqrt{3}-1 )( \sqrt{5}-1 ) \sqrt{\sqrt{5}+5}}{16} \\
\cos39°=\displaystyle\frac{ \sqrt{2}( \sqrt{3}-1 )( \sqrt{5}+1 ) + ( \sqrt{3}+1 )( \sqrt{5}-1 ) \sqrt{\sqrt{5}+5}}{16}
\end{cases}
\\
\begin{cases}
\sin42°=\displaystyle\frac{ \sqrt{2}\sqrt{3}\sqrt{\sqrt{5}+5} - (\sqrt{5}-1) }{8} \\
\cos42°=\displaystyle\frac{ \sqrt{2}\sqrt{\sqrt{5}+5} + \sqrt{3}(\sqrt{5}-1) }{8}
\end{cases}
\\
\begin{cases}
\sin45°=\displaystyle\frac{ \sqrt{ 2 } }{ 2 } \\
\cos45°=\displaystyle\frac{ \sqrt{ 2 } }{ 2 }
\end{cases}
\)
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