Tangens — qarşı katetin qonşu katetə olan nisbətinə deyilir. İfadəsi: tan α = | B C | | A B | = sin α cos α {\displaystyle \tan \alpha ={\frac {|BC|}{|AB|}}={\frac {\sin \alpha }{\cos \alpha }}} =1/ctg
y = tan α {\displaystyle y=\tan \alpha } funksiyası bütün ədəd oxunda artır. y = tan α {\displaystyle y=\tan \alpha } funksiyasının periodu π {\displaystyle \pi } -dir.
tan ( 90 − α ) = tan α {\displaystyle \tan(90-\alpha )=\tan \alpha }
tan ( 90 + α ) = − cot α {\displaystyle \tan(90+\alpha )=-\cot \alpha }
tan ( 180 − α ) = − tan α {\displaystyle \tan(180-\alpha )=-\tan \alpha }
tan ( 180 + α ) = tan α {\displaystyle \tan(180+\alpha )=\tan \alpha }
tan ( 270 − α ) = cot α {\displaystyle \tan(270-\alpha )=\cot \alpha }
tan ( 270 + α ) = − cot α {\displaystyle \tan(270+\alpha )=-\cot \alpha }
tan ( 360 − α ) = − tan α {\displaystyle \tan(360-\alpha )=-\tan \alpha }
tan ( 360 + α ) = tan α {\displaystyle \tan(360+\alpha )=\tan \alpha }
tan 2 α = 2 tan α 1 − tan 2 α {\displaystyle \tan 2\alpha ={\frac {2\tan \alpha }{1-\tan ^{2}\alpha }}}
tan 3 α = 3 tan α − tan 3 α 1 − 3 tan 2 α {\displaystyle \tan 3\alpha ={\frac {3\tan \alpha -\tan ^{3}\alpha }{1-3\tan ^{2}\alpha }}}
tan ( α + β ) = tan α + tan β 1 − tan α ∗ tan β {\displaystyle \tan(\alpha +\beta )={\frac {\tan \alpha +\tan \beta }{1-\tan \alpha *\tan \beta }}}
tan ( α − β ) = tan α − tan β 1 + tan α ∗ tan β {\displaystyle \tan(\alpha -\beta )={\frac {\tan \alpha -\tan \beta }{1+\tan \alpha *\tan \beta }}}
tan α + tan β = sin ( α + β ) cos α ∗ cos β {\displaystyle \tan \alpha +\tan \beta ={\frac {\sin(\alpha +\beta )}{\cos \alpha *\cos \beta }}}
tan α − tan β = sin ( α − β ) cos α ∗ cos β {\displaystyle \tan \alpha -\tan \beta ={\frac {\sin(\alpha -\beta )}{\cos \alpha *\cos \beta }}}
