binti tri kholifah: rumus trigonometri

Rumus Trigonometri Pada Segitiga

Untuk Segitiga Sembarang
1. Aturan Sinus

$\inline \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

2. Aturan Cosinus

$\inline a^{2}=b^{2}+c^{2}-2bc \cos A$

Rumus Identitas:

$\inline \sin ^{2}x+\cos ^{2}x=1$

$\inline 1+\tan^{2}x=\sec ^{2}x$
$\inline 1+\cot^{2}x=\csc ^{2}x$

Sudut Ganda
$\inline \sin 2x=2\sin x\cos x$
$\inline \cos 2x=\cos ^{2}x-\sin ^{2}x$
$\inline \cos 2x=2\cos ^{2}x-1$
$\inline \cos 2x=1-2\sin ^{2}x$
$\inline \tan 2x=\frac{2\tan x}{1-\tan ^{2}x}$

Jumlah dan Selisih Sudut
$\inline \sin \left (A+B \right )=\sin A\cos B+\cos A\sin B$
$\inline \sin \left (A-B \right )=\sin A\cos B-\cos A\sin B$
$\inline \cos \left ( A+B \right )=\cos A\cos B-\sin A\sin B$
$\inline \cos \left ( A-B \right )=\cos A\cos B+\sin A\sin B$
$\inline \tan \left ( A+B \right )=\frac{\tan A+\tan B}{1-\tan A\tan B}$
$\inline \tan \left ( A-B \right )=\frac{\tan A-\tan B}{1+\tan A\tan B}$

Jumlah dan Selisih Fungsi Trigonometri
$\inline \sin A+\sin B=2\sin \frac{1}{2}\left ( A+B \right )\cos \frac{1}{2}\left ( A-B \right )$
$\inline \sin A-\sin B=2\cos \frac{1}{2}\left ( A+B \right )\sin \frac{1}{2}\left ( A-B \right )$
$\inline \cos A+\cos B=2\cos \frac{1}{2}\left ( A+B \right )\cos \frac{1}{2}\left ( A-B \right )$
$\inline \cos A-\cos B=-2\sin \frac{1}{2}\left ( A+B \right )\sin \frac{1}{2}\left ( A-B \right )$

Perkalian Fungsi Trigonometri
$\inline 2\sin A\cos B=\sin \left ( A+B \right )+\sin \left ( A-B \right )$
$\inline 2\cos A\sin B=\sin \left ( A+B \right )-\sin \left ( A-B \right )$
$\inline 2\cos A\cos B=\cos \left ( A+B \right )+\cos \left ( A-B \right )$
$\inline -2\sin A\sin B=\cos \left ( A+B \right )-\cos \left ( A-B \right )$

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Kamis, 27 Januari 2011

rumus trigonometri

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