Tangens — qarşı katetin qonşu katetə olan nisbətinə deyilir. İfadəsi: tanα=|BC||AB|=sinαcosα{\displaystyle \tan \alpha ={\frac {|BC|}{|AB|}}={\frac {\sin \alpha }{\cos \alpha }}}=1/ctg
y=tanα{\displaystyle y=\tan \alpha } funksiyası bütün ədəd oxunda artır. y=tanα{\displaystyle y=\tan \alpha } funksiyasının periodu π{\displaystyle \pi } -dir.
tan(90−α)=tanα{\displaystyle \tan(90-\alpha )=\tan \alpha }
tan(90+α)=−cotα{\displaystyle \tan(90+\alpha )=-\cot \alpha }
tan(180−α)=−tanα{\displaystyle \tan(180-\alpha )=-\tan \alpha }
tan(180+α)=tanα{\displaystyle \tan(180+\alpha )=\tan \alpha }
tan(270−α)=cotα{\displaystyle \tan(270-\alpha )=\cot \alpha }
tan(270+α)=−cotα{\displaystyle \tan(270+\alpha )=-\cot \alpha }
tan(360−α)=−tanα{\displaystyle \tan(360-\alpha )=-\tan \alpha }
tan(360+α)=tanα{\displaystyle \tan(360+\alpha )=\tan \alpha }
tan2α=2tanα1−tan2α{\displaystyle \tan 2\alpha ={\frac {2\tan \alpha }{1-\tan ^{2}\alpha }}}
tan3α=3tanα−tan3α1−3tan2α{\displaystyle \tan 3\alpha ={\frac {3\tan \alpha -\tan ^{3}\alpha }{1-3\tan ^{2}\alpha }}}
tan(α+β)=tanα+tanβ1−tanα∗tanβ{\displaystyle \tan(\alpha +\beta )={\frac {\tan \alpha +\tan \beta }{1-\tan \alpha *\tan \beta }}}
tan(α−β)=tanα−tanβ1+tanα∗tanβ{\displaystyle \tan(\alpha -\beta )={\frac {\tan \alpha -\tan \beta }{1+\tan \alpha *\tan \beta }}}
tanα+tanβ=sin(α+β)cosα∗cosβ{\displaystyle \tan \alpha +\tan \beta ={\frac {\sin(\alpha +\beta )}{\cos \alpha *\cos \beta }}}
tanα−tanβ=sin(α−β)cosα∗cosβ{\displaystyle \tan \alpha -\tan \beta ={\frac {\sin(\alpha -\beta )}{\cos \alpha *\cos \beta }}}
