Posted by Risyda Itsna Sari (28)
Blog IPA 6 SMANIK
Rumus untuk sudut rangkap, sudut tengahan, rumus  (3\alpha), dan perkalian pada Trigonometri 

Rumus sudut rangkap

\sin(2\alpha)=2\sin\alpha\cos\alpha=\frac{2\tan\alpha}{1+\tan^{2}\alpha}
\cos(2\alpha)=\cos^{2}\alpha-\sin^{2}\alpha=1-2\sin^{2}\alpha=2\cos^{2}\alpha-1
\cos(2\alpha)=\frac{1-\tan^{2}\alpha}{1+\tan^{2}\alpha}
\tan(2\alpha)=\frac{2\tan\alpha}{1-\tan^{2}\alpha}
\tan(2\alpha)=\frac{2 \cot \alpha}{\cot^{2}\alpha-1}=\frac{2}{\cot \alpha - \tan\alpha}

Rumus setengah sudut

\sin\frac{\alpha}{2}=\pm\sqrt{\frac{1-\cos\alpha}{2}}
\cos\frac{\alpha}{2}=\pm\sqrt{\frac{1+\cos\alpha}{2}}
\tan\frac{\alpha}{2}=\pm\sqrt{\frac{1-\cos\alpha}{1+\cos\alpha}}=\frac{\sin\alpha}{1+\cos\alpha}
\tan\frac{\alpha}{2}=\frac{1-\cos\alpha}{\sin\alpha}

rumus untuk sudut (3\alpha)

\sin(3\alpha)= 3\sin\alpha-4\sin^{3}\alpha
\cos(3\alpha)= 4\cos^{3}\alpha-3\cos\alpha
\tan(3\alpha)=\frac{3\tan\alpha-\tan^{3}\alpha}{1-3\tan^{2}\alpha}

Rumus perkalian

2\cos \alpha \cos \beta = \cos (\alpha+\beta)+\cos(\alpha-\beta)
2\sin \alpha \sin \beta = -\cos (\alpha+\beta)+\cos(\alpha-\beta)
2\sin \alpha \cos \beta = \sin (\alpha+\beta)+\sin(\alpha-\beta)
2\cos \alpha \sin \beta = \sin (\alpha+\beta)-\sin(\alpha-\beta)
\sin (\alpha + \beta).\sin(\alpha-\beta) = \sin^{2}\alpha-\sin^{2}\beta=\cos^{2}\beta-\cos^{2}\alpha
\cos (\alpha + \beta).\cos(\alpha-\beta) = \cos^{2}\alpha-\sin^{2}\beta=\cos^{2}\beta-\sin^{2}\alpha.


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