## 2016年5月5日木曜日

### 数学 – 円の中にひそむ関数 - 三角関数 – (三角関数の合成)

• 数式入力ソフト(TeX, MathML): MathType
• MathML対応ブラウザ: Firefox、Safari
• MathML非対応ブラウザ(Edge/Internet Explorer, Google Chrome...)用JavaScript Library: MathJax

1. $\begin{array}{l}\mathrm{cos}\alpha =\frac{\sqrt{3}}{2},\mathrm{sin}\alpha =-\frac{1}{2}\\ \alpha =\frac{11}{6}\pi \\ 2\mathrm{sin}\theta \mathrm{cos}\alpha +2\mathrm{cos}\theta \mathrm{sin}\alpha \\ 2\mathrm{sin}\left(\theta +\frac{11}{6}\pi \right)\end{array}$

2. $\begin{array}{l}\mathrm{cos}\alpha =\frac{3}{5},\mathrm{sin}\alpha =\frac{4}{5}\\ 5\mathrm{sin}\theta \mathrm{cos}\alpha +5\mathrm{cos}\theta \mathrm{sin}\alpha \\ =5\mathrm{sin}\left(\theta +\alpha \right)\end{array}$

3. $\begin{array}{l}\mathrm{cos}\beta =\frac{12}{13},\mathrm{sin}\beta =-\frac{5}{13}\\ -13\mathrm{sin}\beta \mathrm{sin}\theta +13\mathrm{cos}\beta \mathrm{cos}\theta \\ =-13\left(\mathrm{cos}\theta \mathrm{cos}\beta -\mathrm{sin}\theta \mathrm{sin}\beta \right)\\ =-13\mathrm{cos}\left(\theta +\beta \right)\end{array}$

4. $\begin{array}{l}\mathrm{cos}\beta =\frac{1}{\sqrt{2}},\mathrm{sin}\beta =\frac{1}{\sqrt{2}}\\ \beta =\frac{\pi }{4}\\ \sqrt{2}\mathrm{cos}\beta \mathrm{cos}\theta -\sqrt{2}\mathrm{sin}\beta \mathrm{sin}\theta \\ =\sqrt{2}\mathrm{cos}\left(\theta +\beta \right)\\ =\sqrt{2}\mathrm{cos}\left(\theta +\frac{\pi }{4}\right)\end{array}$