Matematika SMA: rumus trigonometri

A. Rumus Trigonometri untuk Jumlah dan Selisih Dua Sudut
$\inline \dpi{100} \fn_cm 1.\: \sin \, (\alpha +\beta )=\sin \, \alpha \cos \beta +\cos \, \alpha \sin \, \beta$
$\inline \dpi{100} \fn_cm 2.\: \sin \, (\alpha -\beta )=\sin \alpha \, \cos \, \beta -\cos \, \alpha\, \sin \beta$
$\inline \dpi{100} \fn_cm 3.\: \cos (\alpha +\beta )=\cos \, \alpha \cos \, \beta -\sin \, \alpha \sin \, \beta$
$\inline \dpi{100} \fn_cm 4.\: \cos (\alpha -\beta )=\cos \, \alpha \cos \, \beta +\sin \, \alpha \sin \, \beta$
$\inline \dpi{100} \fn_cm 5.\: \tan (\alpha +\beta )= \frac{\tan \, \alpha +\tan \, \beta }{1-\tan \, \alpha \tan \beta }$
$\inline \dpi{100} \fn_cm 6.\: \tan (\alpha -\beta )= \frac{\tan \, \alpha -\tan \, \beta }{1+\tan \, \alpha \tan \beta }$

B. Rumus Trigonometri Sudut Ganda
$\inline \fn_cm 1.\: \sin \, 2\alpha =2\sin \, \alpha \cos \, \alpha$
$\small \dpi{100} \fn_cm 2.   \cos 2\alpha =\cos ^{2}\, \alpha -\sin ^{2}\alpha$
$\small \dpi{100} \fn_cm 3.   \cos \, 2\alpha =2\cos ^{2}\alpha -1$
$\small \dpi{100} \fn_cm 4. \cos \, 2\alpha =1-2\sin ^{2}\alpha$
$\small \dpi{100} \fn_cm 5. \tan \, 2\alpha =\frac{2\tan \, \alpha }{1-\tan ^{2}\alpha }$

C. Rumus Perkalian Sinus dan Kosinus
$\small \dpi{100} \fn_cm 1.\: 2\sin \, \alpha \, \cos \beta =\sin (\alpha +\beta )+\sin (\alpha -\beta )$
$\small \dpi{100} \fn_cm 2.\: 2\cos \, \alpha \, \, \sin \, \beta =\sin (\alpha +\beta )-\sin (\alpha -\beta )$
$\small \dpi{100} \fn_cm 3.\: 2\cos \, \alpha \cos \, \beta =\cos (\alpha +\beta )+\cos (\alpha -\beta )$
$\small \dpi{100} \fn_cm 4.\: 2\sin \, \alpha \sin \, \beta =\cos (\alpha -\beta )-\cos (\alpha +\beta )$    atau
    $\small \dpi{100} \fn_cm -2\sin \, \alpha \sin \, \beta =\cos (\alpha +\beta )-\cos (\alpha -\beta )$

D. Rumus Jumlah dan Selisih
$\inline \dpi{100} \fn_cm 1.\: \sin \, \alpha +\sin \, \beta =2\sin \frac{1}{2}(\alpha +\beta )\cos \frac{1}{2}(\alpha -\beta )$
$\inline \dpi{100} \fn_cm 2.\: \sin \, \alpha -\sin \, \beta =2\cos \frac{1}{2}(\alpha +\beta )\sin \frac{1}{2}(\alpha -\beta )$
$\inline \dpi{100} \fn_cm 3.\: \cos \, \alpha +\cos \, \beta =2\cos \frac{1}{2}(\alpha +\beta )\cos \frac{1}{2}(\alpha -\beta )$
$\inline \dpi{100} \fn_cm 4.\: \cos \, \alpha -\cos \, \beta =-2\sin \frac{1}{2}(\alpha +\beta )\sin \frac{1}{2}(\alpha -\beta )$
$\inline \dpi{100} \fn_cm 5.\: \tan \, \alpha +\tan \, \beta =\frac{2\sin \, (\alpha +\beta )}{\cos (\alpha +\beta )+\cos (\alpha -\beta )}$
$\inline \dpi{100} \fn_cm 5.\: \tan \, \alpha -\tan \, \beta =\frac{2\sin \, (\alpha -\beta )}{\cos (\alpha +\beta )+\cos (\alpha -\beta )}$

E. Rumus Sudut Tengahan
$\inline \fn_cm 1.\: \: \sin \frac{1}{2}\alpha =\pm \frac{1}{2}\sqrt{2(1-\cos \alpha )}$
$\inline \fn_cm 2.\: \: \cos \frac{1}{2}\alpha =\pm \frac{1}{2}\sqrt{2(1+\cos \alpha )}$
$\inline \fn_cm 3.\: \: \tan \frac{1}{2}\alpha =\pm \sqrt{\frac{1-\cos \, \alpha }{1+\cos \, \alpha }}$
$\inline \fn_cm 4.\: \: \tan \frac{1}{2}\alpha =\frac{\sin \, \alpha }{1+\cos \, \alpha }$
$\inline \fn_cm 5.\: \: \tan \frac{1}{2}\alpha =\frac{1-\cos \, \alpha }{\sin \, \alpha }$

Matematika SMA

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Selasa, 16 Agustus 2011

Rumus-rumus Trigonometri