Name given to certain relationships that exist between various trigonometric ratios.
Symbol
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 :
- \(\sin^2 (θ) + \cos^2 (θ) = 1\)
- \(1 + \tan^2 (θ) = \sec^2 (θ)\)
- \(\cot^2 (θ) + 1 = \textrm{csc}^2 (θ) \)