[tex]Wszystkie~potrzebne~"wzory":\\I.~\cos^2\alpha+\sin^2\alpha=1\\II.~tg~\alpha=\frac{\sin\alpha}{\cos\alpha}\\III.~ctg~\alpha=\frac1{tg~\alpha}[/tex]
[tex]\cos^2\alpha+\sin^2\alpha=1\\\\(\frac{\sqrt{2}}{5})^2+\sin^2\alpha=1\\\frac{2}{25}+\sin^2\alpha=1\\\sin^2\alpha=1-\frac{2}{25}\\\sin^2\alpha=\frac{23}{25}|\sqrt{~}\\\sin\alpha=\frac{\sqrt{23}}{5}~~~~~~~~~\vee~~~~~~~\sin\alpha=-\frac{\sqrt{23}}{5}\\[/tex]
[tex]tg~\alpha=\frac{\sin\alpha}{\cos\alpha}~~~~~~~~~~~~~~~~~~~~tg~\alpha=\frac{\sin\alpha}{\cos\alpha}\\\\tg~\alpha=\dfrac{\frac{\sqrt{23}}{5}}{\frac{\sqrt{2}}{5}}~~~~~~~~~~~~~~~~~~~~tg~\alpha=\dfrac{-\frac{\sqrt{23}}{5}}{\frac{\sqrt{2}}{5}}\\tg~\alpha=\frac{\sqrt{23}}{5}:\frac{\sqrt{2}}{5}~~~~~~~~~~~~~~tg~\alpha=-\frac{\sqrt{23}}{5}:\frac{\sqrt{2}}{5}\\tg~\alpha=\frac{\sqrt{23}}{5}\cdot\frac{5}{\sqrt{2}}~~~~~~~~~~~~~~tg~\alpha=-\frac{\sqrt{23}}{5}\cdot\frac{5}{\sqrt{2}}[/tex]
[tex]tg~\alpha=\frac{\sqrt{23}}{\sqrt{2}}~~~~~~~~~~~~~~~~~~~~tg~\alpha=-\frac{\sqrt{23}}{\sqrt{2}}\\tg~\alpha=\frac{\sqrt{23}\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}~~~~~~~~~~~~~~~~tg~\alpha=-\frac{\sqrt{23}\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}~~~~~~~~~~~~~~~~\\tg~\alpha=\frac{\sqrt{46}}{2}~~~~~~~~\vee~~~~~~~~~tg~\alpha=-\frac{\sqrt{46}}{2}[/tex]
[tex]ctg~\alpha=\frac1{tg~\alpha}~~~~~~~~~~~~~~~~~~~~ctg~\alpha=\frac1{tg~\alpha}\\\\ctg~\alpha=\dfrac1{\frac{\sqrt{46}}{2}}~~~~~~~~~~~~~~~~~~~ctg~\alpha=\dfrac1{-\frac{\sqrt{46}}{2}}\\ctg~\alpha=\frac{2}{\sqrt{46}}~~~~~~~~~~~~~~~~~~~ctg~\alpha=-\frac{2}{\sqrt{46}}}\\ctg~\alpha=\frac{2\cdot\sqrt{46}}{\sqrt{46}\cdot\sqrt{46}}~~~~~~~~~~~~~~ctg~\alpha=-\frac{2\cdot\sqrt{46}}{\sqrt{46}\cdot\sqrt{46}}}\\ctg~\alpha=\frac{2\sqrt{46}}{46}~~~~~~~\vee~~~~~~~~ctg~\alpha=-\frac{2\sqrt{46}}{46}}[/tex]
Są dwie odpowiedzi:
- [tex]\sin\alpha=\frac{\sqrt{23}}{5}~~~~\cos\alpha=\frac{\sqrt2}{5}~~~~tg~\alpha=\frac{\sqrt{46}}{2}~~~~ctg~\alpha=\frac{2\sqrt{46}}{46}[/tex]
- [tex]\sin\alpha=-\frac{\sqrt{23}}{5}~~~~\cos\alpha=\frac{\sqrt2}{5}~~~~tg~\alpha=-\frac{\sqrt{46}}{2}~~~~ctg~\alpha=-\frac{2\sqrt{46}}{46}[/tex]
