Trigonometry - Identities

Identities are equations that are true for all values of the variables involved.This lesson is meant to summarize the various identities that are used in relation to Trigonometry.

Trigonometric Identities

Quotient Reciprocol Pythagorean Compound Angle
\(\tan\theta = \cfrac{\sin\theta}{\cos\theta}\) \(\csc\theta = \cfrac{1}{\sin\theta}\) \(\sin²\theta + \cos²\theta = 1\) \(\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\)
\(\cot\theta = \cfrac{\cos\theta}{\sin\theta}\) \(\sec\theta = \cfrac{1}{\cos\theta}\) \(\sec²\theta - \tan²\theta = 1\) \(\sin(x-y) = \sin(x)\cos(y) - \cos(x)\sin(y)\)
  \(\cot\theta = \cfrac{1}{\tan\theta}\) \(\csc²\theta + \cot²\theta = 1\) \(\cos(x+y) = \cos(x)\cos(y) - \sin(x)\sin(y)\)
      \(\cos(x-y) = \cos(x)\cos(y) + \sin(x)\sin(y)\)