Calculus/Table of Trigonometry

DefinitionsEdit

  • \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}

Pythagorean IdentitiesEdit

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

Double Angle IdentitiesEdit

  • \sin(2 x)=  2\sin x \cos x \
  • \cos(2 x)=  \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}

Angle Sum IdentitiesEdit

\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}

Product-to-sum identitiesEdit

\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} \;

See alsoEdit


Last modified on 28 May 2011, at 16:47