基本的な三角形と三角比

正方形の半分
各辺の比が $3$\displaystyle{ 1:1:\sqrt{2} }$ の直角二等辺三角形 $image1$
$3$\displaystyle{\begin{array}{lll}\sin 45^\circ =\frac{\hspace{2} \text{BC} \hspace{2}}{\hspace{2} \text{AB} \hspace{2}}=\frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{2} \hspace{2}}& \vspace{6}\\ & \vspace{6}\\ \cos 45^\circ =\frac{\hspace{2} \text{AC} \hspace{2}}{\hspace{2} \text{AB} \hspace{2}}=\frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{2} \hspace{2}}& \vspace{6}\\ & \vspace{6}\\ \tan 45^\circ =\frac{\hspace{2} \text{BC} \hspace{2}}{\hspace{2} \text{AC} \hspace{2}}=\frac{\hspace{2}1\hspace{2}}{\hspace{2}1\hspace{2}}& \vspace{6}\\ \end{array}}$

正三角形の半分
各辺の比が $3$\displaystyle{ 1:2:\sqrt{3} }$ の直角三角形 $image2$
$3$\displaystyle{{\theta}=30^\circ }$ のとき，

$3$\displaystyle{\begin{array}{lll}\sin 30^\circ =\frac{\hspace{2} \text{BC} \hspace{2}}{\hspace{2} \text{AB} \hspace{2}}=\frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}}& \vspace{6}\\ & \vspace{6}\\ \cos 30^\circ =\frac{\hspace{2} \text{AC} \hspace{2}}{\hspace{2} \text{AB} \hspace{2}}=\frac{\hspace{2} \sqrt{3} \hspace{2}}{\hspace{2}2\hspace{2}}& \vspace{6}\\ & \vspace{6}\\ \tan 30^\circ =\frac{\hspace{2} \text{BC} \hspace{2}}{\hspace{2} \text{AC} \hspace{2}}=\frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{3} \hspace{2}}& \vspace{6}\\ \end{array}}$

$3$\displaystyle{{\theta}=60^\circ }$ のとき，

$3$\displaystyle{\begin{array}{lll}\sin 60^\circ =\frac{\hspace{2} \text{AC} \hspace{2}}{\hspace{2} \text{AB} \hspace{2}}=\frac{\hspace{2} \sqrt{3} \hspace{2}}{\hspace{2}2\hspace{2}}& \vspace{6}\\ & \vspace{6}\\ \cos 60^\circ =\frac{\hspace{2} \text{BC} \hspace{2}}{\hspace{2} \text{AB} \hspace{2}}=\frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}}& \vspace{6}\\ & \vspace{6}\\ \tan 60^\circ =\frac{\hspace{2} \text{AC} \hspace{2}}{\hspace{2} \text{BC} \hspace{2}}=\frac{\hspace{2} \sqrt{3} \hspace{2}}{\hspace{2}1\hspace{2}}& \vspace{6}\\ \end{array}}$

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