Szczegółowe wyjaśnienie:
Patrz załącznik.
1.
[tex]x^2+5^2=13^2\\\\x^2+25=169\qquad|-25\\\\x^2=144\to x=\sqrt{144}\\\\x=12[/tex]
[tex]\sin\alpha=\dfrac{5}{13}\\\\\cos\alpha=\dfrac{12}{13}\\\\\text{tg}\alpha=\dfrac{5}{12}\\\\\text{ctg}\alpha=\dfrac{12}{5}[/tex]
2.
[tex]y^2=3^2+4^2\\\\y^2=9+16\\\\y^2=25\to y=\sqrt{25}\\\\y=5[/tex]
[tex]\sin\alpha=\dfrac{3}{5}\\\\\cos\alpha=\dfrac{4}{5}\\\\\text{tg}\alpha=\dfrac{3}{4}\\\\\text{ctg}\alpha=\dfrac{4}{3}[/tex]
3.
[tex]z^2+36^2=39^2\\\\z^2+1296=1521\qquad|-1296\\\\z^2=225\to z=\sqrt{225}\\\\z=15[/tex]
[tex]\sin\alpha=\dfrac{15}{39}\\\\\cos\alpha=\dfrac{36}{39}\\\\\text{tg}\alpha=\dfrac{15}{36}=\dfrac{5}{12}\\\\\text{ctg}\alpha=\dfrac{36}{15}=\dfrac{12}{5}[/tex]
