| 關鍵字 |
說明 |
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| 複角公式 |
\(\sin (\alpha + \beta ) = \sin \alpha \cos \beta + \cos \alpha \sin \beta \)
\(\sin (\alpha - \beta ) = \sin \alpha \cos \beta - \cos \alpha \sin \beta \)
\(\cos (\alpha + \beta ) = \cos \alpha \cos \beta - \sin \alpha \sin \beta \)
\(\cos (\alpha - \beta ) = \cos \alpha \cos \beta + \sin \alpha \sin \beta \)
\(\tan (\alpha + \beta ) = \frac{{\tan \alpha + \tan \beta }}{{1 - \tan \alpha \tan \beta }}\) ， \(\tan (\alpha - \beta ) = \frac{{\tan \alpha - \tan \beta }}{{1 + \tan \alpha \tan \beta }}\)
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| 倍角公式 |
倍角公式是複角公式的特例，只要令 \(\alpha = \beta = \theta \) 即可
\(\sin 2\theta = 2\sin \theta \cos \theta \)
\(\cos 2\theta = {\cos ^2}\theta - {\sin ^2}\theta \)
\( = 2{\cos ^2}\theta - 1\)
\( = 1 - 2{\sin ^2}\theta \) |
| 三倍角公式 |
(1) \(\sin 3\theta = 3\sin \theta - 4{\sin ^3}\theta \)
(2) \(\cos 3\theta = 4{\cos ^3}\theta - 3\cos \theta \) |
| 積化和差 |
\(2\sin \alpha \cos \beta = \sin (\alpha + \beta ) + \sin (\alpha - \beta )\)
\(2\cos \alpha \cos \beta = \cos (\alpha + \beta ) + \cos (\alpha - \beta )\)
\(2\sin \alpha \sin \beta = \cos (\alpha - \beta ) - \cos (\alpha + \beta )\) |
