Trigonometric Identity

Trigonometric Identity

Name given to certain relationships that exist between various trigonometric ratios.


We sometimes use the symbol “≡” for trigonometric identities.

Some of these identities are fundamental and result from the study of the right triangle :


sin (A) = \(\dfrac{a}{c}\),   csc (A) = \(\dfrac{c}{a}\),   cos (A) = \(\dfrac{b}{c}\),   sec (A) = \(\dfrac{c}{b}\),   tan (A) = \(\dfrac{a}{b}\),   cot (A) = \(\dfrac{b}{a}\)

Other identities result from the study of the trigonometric circle :

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

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