Odpowiedź:
b)
[tex] \sin( \alpha ) = \frac{2}{2 \sqrt{5} } = \frac{1}{ \sqrt{5} } = \frac{ \sqrt{5} }{5} \\ \sin( \beta ) = \frac{4}{2 \sqrt{5} } = \frac{2}{ \sqrt{5} } = \frac{2 \sqrt{5} }{5} \\ \cos( \alpha ) = \frac{4}{2 \sqrt{5} } = \frac{2}{ \sqrt{5} } = \frac{2 \sqrt{5} }{5} \\ \cos( \beta ) = \frac{2}{2 \sqrt{5} } = \frac{1}{ \sqrt{5} } = \frac{ \sqrt{5} }{5} \\ \tan( \alpha ) = \frac{2}{4} = \frac{1}{2} \\ \tan( \beta ) = \frac{4}{2} = 2[/tex]
c)
[tex] \sin( \alpha ) = \frac{2 \sqrt{3} }{5} \\ \sin( \beta ) = \frac{ \sqrt{13} }{5} \\ \cos( \alpha ) = \frac{ \sqrt{13} }{5} \\ \cos( \beta ) = \frac{2 \sqrt{3} }{5} \\ \tan( \alpha ) = \frac{2 \sqrt{3} }{ \sqrt{13} } = \frac{2 \sqrt{39} }{13} \\ \tan( \beta ) = \frac{ \sqrt{13} }{2 \sqrt{3} } = \frac{ \sqrt{39} }{12} [/tex]
