Rysunek pomocniczy:

Zauważmy, że:

$\sin {30}^{\circ }=\frac{a}{2a}=\frac{1}{2}$  

$\cos {30}^{\circ }=\frac{a\sqrt{3}}{2a}=\frac{\sqrt{3}}{2}$  

$\mathrm{tg}{30}^{\circ }=\frac{a}{a\sqrt{3}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$  

oraz

$\sin {60}^{\circ }=\frac{a\sqrt{3}}{2}a=\frac{\sqrt{3}}{2}$  

$\cos {60}^{\circ }=\frac{a}{2a}=\frac{1}{2}$  

$\mathrm{tg}{60}^{\circ }=\frac{a\sqrt{3}}{a}=\sqrt{3}$  

 

$\sin {45}^{\circ }=\frac{a}{a\sqrt{2}}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}$   

$\cos {45}^{\circ }=\frac{a}{a\sqrt{2}}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}$  

$\mathrm{tg}{45}^{\circ }=\frac{a}{a}=1$    

 

Uzupełniamy tabelkę: