Rumus trigonometri

Hubungan fungsi trigonometri

$\sin ^{2}A+\cos ^{2}A=1\,$

$1+\tan ^{2}A={\frac {1}{\cos ^{2}A}}=\sec ^{2}A\,$

$1+\cot ^{2}A=\csc ^{2}A\,$

$\tan A={\frac {\sin A}{\cos A}}\,$

Penjumlahan

$\sin(A+B)=\sin A\cos B+\cos A\sin B\,$

$\sin(A-B)=\sin A\cos B-\cos A\sin B\,$

$\cos(A+B)=\cos A\cos B-\sin A\sin B\,$

$\cos(A-B)=\cos A\cos B+\sin A\sin B\,$

$\tan(A+B)={\frac {\tan A+\tan B}{1-\tan A\tan B}}\,$

$\tan(A-B)={\frac {\tan A-\tan B}{1+\tan A\tan B}}\,$

Rumus sudut rangkap dua

$\sin 2A=2\sin A\cos A\,$

$\cos 2A=\cos ^{2}A-\sin ^{2}A=2\cos ^{2}A-1=1-2\sin ^{2}A\,$

$\tan 2A={2\tan A \over 1-\tan ^{2}A}={2\cot A \over \cot ^{2}A-1}={2 \over \cot A-\tan A}\,$

Rumus sudut rangkap tiga

$\sin 3A=3\sin A-4\sin ^{3}A\,$

$\cos 3A=4\cos ^{3}A-3\cos A\,$

Rumus setengah sudut

$\sin {\frac {A}{2}}=\pm {\sqrt {\frac {1-\cos A}{2}}}\,$

$\cos {\frac {A}{2}}=\pm {\sqrt {\frac {1+\cos A}{2}}}\,$

$\tan {\frac {A}{2}}=\pm {\sqrt {\frac {1-\cos A}{1+\cos A}}}={\frac {\sin A}{1+\cos A}}={\frac {1-\cos A}{\sin A}}\,$

Lihat pula

• Sinus
• Cosinus
• Tangen
• Secan
• Cosecan
• Cotangen