W zadaniu korzystamy z proporcji.

$\text{a)}{30}^{\circ }$  

$\frac{{30}^{\circ }}{{360}^{\circ }}=\frac{x}{2\pi }$  

$x=\frac{\sout{{30}^{\circ }}\cdot 2\pi }{{\sout{{360}^{\circ }}}^{12}}=\frac{{\sout{2}}^1\pi }{{\sout{12}}^6}=\frac{\pi }{6}$   

${30}^{\circ }=\frac{\pi }{6}$  

$\underline{\underline{}}$

$\text{b)}{45}^{\circ }$  

$\frac{{45}^{\circ }}{{360}^{\circ }}=\frac{x}{2\pi }$  

$x=\frac{\sout{{45}^{\circ }}\cdot 2\pi }{{\sout{{360}^{\circ }}}^8}=\frac{{\sout{2}}^1\pi }{{\sout{8}}^4}=\frac{\pi }{4}$   

${45}^{\circ }=\frac{\pi }{4}$   

$\underline{\underline{}}$  

$\text{c)}{72}^{\circ }$  

$\frac{{72}^{\circ }}{{360}^{\circ }}=\frac{x}{2\pi }$  

$x=\frac{\sout{{72}^{\circ }}\cdot 2\pi }{{\sout{{360}^{\circ }}}^5}=\frac{2\pi }{5}$   

${72}^{\circ }=\frac{2\pi }{5}$   

$\underline{\underline{}}$  

$\text{d)}{780}^{\circ }$  

$\frac{{780}^{\circ }}{{360}^{\circ }}=\frac{x}{2\pi }$  

$x=\frac{{\sout{{780}^{\circ }}}^{39}\cdot 2\pi }{{\sout{{360}^{\circ }}}^{18}}=\frac{39\cdot {\sout{2}}^1\pi }{{\sout{18}}^9}=\frac{39}{9}\pi =4\frac{1}{3}\pi$     

${780}^{\circ }=4\frac{1}{3}\pi$    

$\underline{\underline{}}$  

$\text{e)}{11}^{\circ }15{}^{\prime }$  

Zamieńmy 15' na stopnie.

$1^{\circ }=60{}^{\prime }==\Rightarrow 15{}^{\prime }={\left(\frac{1}{4}\right)}^{\circ }={0,25}^{\circ }$    

${11}^{\circ }15{}^{\prime }={11,25}^{\circ }$  

 

$\frac{{11,25}^{\circ }}{{360}^{\circ }}=\frac{x}{2\pi }$   

$x=\frac{{\sout{{11,25}^{\circ }}}^1\cdot 2\pi }{{\sout{{360}^{\circ }}}^{32}}=\frac{{\sout{2}}^1\pi }{{\sout{32}}^{16}}=\frac{\pi }{16}$      

${11}^{\circ }15{}^{\prime }=\frac{\pi }{16}$