Tożsamości trygonometryczne – kąty wypukłe

\mathrm{\sin ^2}\alpha +\cos ^2\alpha =1 sin2 α + cos2 α  =  1

Dla każdego kąta\alpha α takiego, że0^{\circ }\le \alpha \le 180^{\circ }\textrm{:} 0∘  ≤  α  ≤  180∘:
\mathrm{\sin ^2}\alpha +\cos ^2\alpha =1, sin2 α + cos2 α  =  1, \mathrm{\tg }\alpha =\frac{\mathrm{\sin }\alpha }{\mathrm{\cos }\alpha }, tg α  =  sin αcos α, \alpha \neq 90^{\circ } α  ≠  90∘

Jeśli\alpha α jest kątem ostrym, to:
\mathrm{\sin }\mleft(90^{\circ }-\alpha \mright)=\cos \alpha , sin(90∘ − α)  =  cos α, \mathrm{\cos }\mleft(90^{\circ }-\alpha \mright)=\sin \alpha , cos(90∘ − α)  =  sin α, \mathrm{\tg }\mleft(90^{\circ }-\alpha \mright)=\frac{1}{\mathrm{\tg }\alpha } tg(90∘ − α)  =  1tg α

\mathrm{\sin }\mleft(180^{\circ }-\alpha \mright)=\sin \alpha , sin(180∘ − α)  =  sin α, \mathrm{\cos }\mleft(180^{\circ }-\alpha \mright)=-\cos \alpha , cos(180∘ − α)  =  − cos α, \mathrm{\tg }\mleft(180^{\circ }-\alpha \mright)=-\tg \alpha tg(180∘ − α)  =  − tg α