Sprawdzamy wartości funkcji kąta 45°:

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

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

$\text{tg}{45}^{\circ }=\frac{1}{1}=1$  

$\text{ctg}{45}^{\circ }=\frac{1}{1}=1$  

 

Sprawdzamy wartości funkcji kąta 30°:

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

$\cos {30}^{\circ }=\frac{\frac{\sqrt{3}}{2}}{1}=\frac{\sqrt{3}}{2}$   

$\text{tg}{30}^{\circ }=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{{\sout{2}}^1}\cdot \frac{{\sout{2}}^1}{\sqrt{3}}=\frac{1}{\sqrt{3}}=\frac{1\cdot \sqrt{3}}{\sqrt{3}\cdot \sqrt{3}}=\frac{\sqrt{3}}{3}$   

$\text{ctg}{30}^{\circ }=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\sqrt{3}}{{\sout{2}}^1}\cdot {\sout{2}}^1=\sqrt{3}$  

 

Sprawdzamy wartości funkcji kąta 60°:

$\sin {60}^{\circ }=\frac{\frac{\sqrt{3}}{2}}{1}=\frac{\sqrt{3}}{2}$   

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

$\text{tg}{60}^{\circ }=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\sqrt{3}}{{\sout{2}}^1}\cdot {\sout{2}}^1=\sqrt{3}$   

$\text{ctg}{60}^{\circ }=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{{\sout{2}}^1}\cdot \frac{{\sout{2}}^1}{\sqrt{3}}=\frac{1}{\sqrt{3}}=\frac{1\cdot \sqrt{3}}{\sqrt{3}\cdot \sqrt{3}}=\frac{\sqrt{3}}{3}$