Penghargaan Itu Bermula Dari Prestasi: Rumus Trigonometeri

$1. Sin \hspace{2mm}\alpha = \hspace{2mm}\frac {AC}{BC}$
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$2. Cos \hspace{2mm}\alpha = \hspace{2mm}\frac {AB}{BC}$
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$3. Tan \hspace{2mm}\alpha = \hspace{2mm}\frac {AC}{AB}$
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$4. Ctg \hspace{2mm}\alpha = \hspace{2mm}\frac {AB}{AC}$
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$5. Sec \hspace{2mm}\alpha = \hspace{2mm}\frac {BC}{AB}$
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$6. Cosec \hspace{2mm}\alpha = \hspace{2mm}\frac {BC}{AC}$
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Rumus Identitas
$1. Sin \sp{2}\alpha \hspace{2mm}+ cos \sp{2}\alpha \hspace {2mm}= 1$
$2. tan \sp{2}\alpha \hspace{2mm}+ 1 \hspace{2mm}=\hspace{2mm}Sec \sp{2}\alpha$
$3. Ctg \sp{2}\alpha \hspace{2mm}+ 1 \hspace{2mm}=\hspace{2mm}Cosec \sp{2} \alpha$
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Rumus Kebalikan
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$1. Cosec \alpha \hspace{2mm}=\hspace {2mm} \frac {1}{sin \alpha}$
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$2. Sec \alpha \hspace{2mm}=\hspace {2mm} \frac {1}{Cos \alpha}$
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$3. Ctg \alpha \hspace{2mm}=\hspace {2mm} \frac {1}{Tan \alpha}$ Rumus Penjumlahan dan pengurangan
$\sin(\alpha+\beta)=\sin \alpha \cos\beta + \cos\alpha \sin\beta$
$\sin(\alpha-\beta)=\sin \alpha \cos\beta -\cos\alpha \sin\beta$
$\cos(\alpha+\beta)=\cos \alpha \cos\beta - \sin\alpha \sin\beta$
$\cos(\alpha-\beta)=\cos \alpha \cos\beta +\sin\alpha \sin\beta$
$\tan(\alpha+\beta)=\frac{\tan\alpha+\tan\beta}{1-\tan\alpha\tan\beta}$
$\tan(\alpha-\beta)=\frac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}$
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
$2\cos \alpha \cos \beta = \cos (\alpha+\beta)+\cos(\alpha-\beta)$
$2\sin \alpha \sin \beta = -\cos (\alpha+\beta)+\cos(\alpha-\beta)$
$2\sin \alpha \cos \beta = \sin (\alpha+\beta)+\sin(\alpha-\beta)$
$2\cos \alpha \sin \beta = \sin (\alpha+\beta)-\sin(\alpha-\beta)$
$\sin (\alpha + \beta).\sin(\alpha-\beta) = \sin^{2}\alpha-\sin^{2}\beta=\cos^{2}\beta-\cos^{2}\alpha$
$\cos (\alpha + \beta).\cos(\alpha-\beta) = \cos^{2}\alpha-\sin^{2}\beta=\cos^{2}\beta-\sin^{2}\alpha$ .
Rumus Jumlah dan selisih.
$\cos \alpha +\cos \beta = 2\cos\frac{\alpha+\beta}{2}\cos\frac{\alpha-\beta}{2}$
$\cos \alpha -\cos \beta = -2\sin\frac{\alpha+\beta}{2}\sin\frac{\alpha-\beta}{2}$
$\sin \alpha +\sin \beta = 2\sin\frac{\alpha+\beta}{2}\cos\frac{\alpha-\beta}{2}$
$\sin \alpha -\sin \beta = 2\cos\frac{\alpha+\beta}{2}\sin\frac{\alpha-\beta}{2}$
$\tan \alpha +\tan \beta = \frac{\sin(\alpha+\beta)}{\cos\alpha.\cos\beta}$
$\tan \alpha -\tan \beta = \frac{\sin(\alpha-\beta)}{\cos\alpha.\cos\beta}$ .
Grafik fungsi trigonometri
y = sin x

Penghargaan Itu Bermula Dari Prestasi

Jumat, 08 November 2013

Rumus Trigonometeri

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