sin 2 α + cos 2 α = 1 tan α = sin α cos α cot α = cos α sin α sec α = 1 sin α {\displaystyle \,\!\sin ^{2}\alpha +\cos ^{2}\alpha =1\qquad \tan \alpha ={\frac {\sin \alpha }{\cos \alpha }}\qquad \cot \alpha ={\frac {\cos \alpha }{\sin \alpha }}\qquad \sec \alpha ={\frac {1}{\sin \alpha }}} {\displaystyle \,\!} csc α = 1 cos α {\displaystyle \,\!\csc \alpha ={\frac {1}{\cos \alpha }}}
sin α = ± 1 − cos 2 α cos α = ± 1 − sin 2 α sin α = ± tan α 1 + tan 2 α cos α = ± 1 1 + tan 2 α {\displaystyle \,\!\sin \alpha =\pm {\sqrt {1-\cos ^{2}\alpha }}\qquad \cos \alpha =\pm {\sqrt {1-\sin ^{2}\alpha }}\qquad \sin \alpha =\pm {\frac {\tan \alpha }{\sqrt {1+\tan ^{2}\alpha }}}\qquad \cos \alpha =\pm {\frac {1}{\sqrt {1+\tan ^{2}\alpha }}}}
tan ( 180 ∘ − α ) = − tan α {\displaystyle \,\!\qquad \tan(180^{\circ }-\alpha )=-\tan \alpha } sin ( 180 ∘ + α ) = − sin α cos ( 180 ∘ + α ) = − cos α tan ( 180 ∘ + α ) = tan α {\displaystyle \,\!\sin(180^{\circ }+\alpha )=-\sin \alpha \qquad \cos(180^{\circ }+\alpha )=-\cos \alpha \qquad \tan(180^{\circ }+\alpha )=\tan \alpha }