Trigonometric Identities

This comprehensive reference lists all fundamental trigonometric identities with their mathematical formulas. For detailed explanations and worked examples, visit our tutorial on Using Trigonometric Identities.

Fundamental Trigonometric Identities

Pythagorean Identities

  1. \(\sin^2 x + \cos^2 x = 1\)
  2. \(\tan^2 x + 1 = \sec^2 x\)
  3. \(1 + \cot^2 x = \csc^2 x\)

Reciprocal Identities

  1. \(\csc x = \frac{1}{\sin x}\)
  2. \(\sec x = \frac{1}{\cos x}\)
  3. \(\cot x = \frac{1}{\tan x}\)

Quotient Identities

  1. \(\tan x = \frac{\sin x}{\cos x}\)
  2. \(\cot x = \frac{\cos x}{\sin x}\)

Negative Angle Identities

  1. \(\sin(-x) = -\sin x\) (sine is an odd function)
  2. \(\cos(-x) = \cos x\) (cosine is an even function)
  3. \(\tan(-x) = -\tan x\) (tangent is an odd function)

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