Kalkulus/Tabel trigonometri

Definisi

• $\tan(x)={\frac {\sin x}{\cos x}}$
• $\sec(x)={\frac {1}{\cos x}}$
• $\cot(x)={\frac {\cos x}{\sin x}}={\frac {1}{\tan x}}$
• $\csc(x)={\frac {1}{\sin x}}$

Identitas phytagoras

• $\sin ^{2}x+\cos ^{2}x=1\$
• $1+\tan ^{2}(x)=\sec ^{2}x\$
• $1+\cot ^{2}(x)=\csc ^{2}x\$

Identitas sudut ganda

• $\sin(2x)=2\sin x\cos x\$
• $\cos(2x)=\cos ^{2}x-\sin ^{2}x\$
• $\tan(2x)={\frac {2\tan(x)}{1-\tan ^{2}(x)}}$
• $\cos ^{2}(x)={1+\cos(2x) \over 2}$
• $\sin ^{2}(x)={1-\cos(2x) \over 2}$

Identitas sudut penjumlahan

$\sin \left(x+y\right)=\sin x\cos y+\cos x\sin y$

$\sin \left(x-y\right)=\sin x\cos y-\cos x\sin y$

$\cos \left(x+y\right)=\cos x\cos y-\sin x\sin y$

$\cos \left(x-y\right)=\cos x\cos y+\sin x\sin y$

$\sin x+\sin y=2\sin \left({\frac {x+y}{2}}\right)\cos \left({\frac {x-y}{2}}\right)$

$\sin x-\sin y=2\cos \left({\frac {x+y}{2}}\right)\sin \left({\frac {x-y}{2}}\right)$

$\cos x+\cos y=2\cos \left({\frac {x+y}{2}}\right)\cos \left({\frac {x-y}{2}}\right)$

$\cos x-\cos y=-2\sin \left({\frac {x+y}{2}}\right)\sin \left({\frac {x-y}{2}}\right)$

$\tan x+\tan y={\frac {\sin \left(x+y\right)}{\cos x\cos y}}$

$\tan x-\tan y={\frac {\sin \left(x-y\right)}{\cos x\cos y}}$

$\cot x+\cot y={\frac {\sin \left(x+y\right)}{\sin x\sin y}}$

$\cot x-\cot y={\frac {-\sin \left(x-y\right)}{\sin x\sin y}}$

Identitas perkalian menjadi penjumlahan

$\cos \left(x\right)\cos \left(y\right)={\cos \left(x+y\right)+\cos \left(x-y\right) \over 2}\;$

$\sin \left(x\right)\sin \left(y\right)={\cos \left(x-y\right)-\cos \left(x+y\right) \over 2}\;$

$\sin \left(x\right)\cos \left(y\right)={\sin \left(x+y\right)+\sin \left(x-y\right) \over 2}\;$

$\cos \left(x\right)\sin \left(y\right)={\sin \left(x+y\right)-\sin \left(x-y\right) \over 2}\;$

Lihat juga

• Trigonometri