【高校数学Ⅰ】3-1-2 三角比の関係｜要点まとめ

\(=\cos 20^{\circ}\)

\(=\sin 38^{\circ}\)

\(\displaystyle =\frac{1}{\tan 34^{\circ}}\)

\(\cos^2\theta=1-\sin^2\theta\)
\(\displaystyle \ \ \ \ \ \ \ \ \ =1-\left(\frac{2}{3}\right)^2\)
\(\displaystyle \ \ \ \ \ \ \ \ \ =\frac{5}{9}\)
\(\cos\theta>0\)より、
\(\displaystyle \cos\theta=\frac{\sqrt{5}}{3}\)

\(\displaystyle \tan\theta=\frac{\sin\theta}{\cos\theta}\)
\(\displaystyle \ \ \ \ \ \ \ \ =\frac{2}{3}\div\frac{\sqrt{5}}{3}\)
\(\displaystyle \ \ \ \ \ \ \ \ =\frac{2}{\sqrt{5}}\)
\(\displaystyle \ \ \ \ \ \ \ \ =\frac{2\sqrt{5}}{5}\)

\(\displaystyle \cos^2\theta=\frac{1}{1+\tan^2\theta}\)
\(\displaystyle \ \ \ \ \ \ \ \ \ =\frac{1}{1+2^2}\)
\(\displaystyle \ \ \ \ \ \ \ \ \ =\frac{1}{5}\)
\(\cos\theta>0\)より、
\(\displaystyle \cos\theta=\frac{\sqrt{5}}{5}\)

\(\displaystyle \sin\theta=\cos\theta\tan\theta\)
\(\displaystyle \ \ \ \ \ \ \ \ =\frac{\sqrt{5}}{5}\times2\)
\(\displaystyle \ \ \ \ \ \ \ \ =\frac{2\sqrt{5}}{5}\)