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Formulae

General trigonometric identities

Formulae

A list of important general trigonometric identities,

Some more specific identities that relate to the following general diagram,

1/triangle.jpg
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If \inline  A+B+C=180^{\circ}

  • \inline  \displaystyle \tan A + \tan B + \tan C = \tan A \tan B \tan C
  • \inline  \displaystyle \cot \tfrac{1}{2}A + \cot \tfrac{1}{2} B + \cot \tfrac{1}{2} C = \cot \tfrac{1}{2} A \cot \tfrac{1}{2} B \cot \tfrac{1}{2} C
  • \inline  \displaystyle \sin A + \sin B + \sin C = 4 \cos \tfrac{1}{2} A \cos \tfrac{1}{2} B \cos \tfrac{1}{2} C
  • \inline  \displaystyle \cos A + \cos B + \cos C -1 = 4 \sin \tfrac{1}{2} A \sin \tfrac{1}{2} B \sin \tfrac{1}{2} C

where

  • R stands for the curcum-radius of the triangle ABC

To avoid doubt (and for those new to maths):
  • \inline  \cot \theta = 1 / \tan \theta
  • \inline  \csc \theta = 1 / \sin \theta
  • \inline  \sec \theta = 1 / \cos \theta