Trigonometric Identity
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) = [latex]\dfrac{a}{c}[/latex], csc (A) = [latex]\dfrac{c}{a}[/latex], cos (A) = [latex]\dfrac{b}{c}[/latex], sec (A) = [latex]\dfrac{c}{b}[/latex], tan (A) = [latex]\dfrac{a}{b}[/latex], cot (A) = [latex]\dfrac{b}{a}[/latex]
Other identities result from the study of the trigonometric circle :
sin (A) = [latex]\dfrac{a}{c}[/latex], csc (A) = [latex]\dfrac{c}{a}[/latex], cos (A) = [latex]\dfrac{b}{c}[/latex], sec (A) = [latex]\dfrac{c}{b}[/latex], tan (A) = [latex]\dfrac{a}{b}[/latex], cot (A) = [latex]\dfrac{b}{a}[/latex]
Other identities result from the study of the trigonometric circle :
- [latex]\sin^2 (θ) + \cos^2 (θ) = 1[/latex]
- [latex]1 + \tan^2 (θ) = \sec^2 (θ)[/latex]
- [latex]\cot^2 (θ) + 1 = \textrm{csc}^2 (θ) [/latex]