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 }}}