Odpowiedź:
Szczegółowe wyjaśnienie:
[tex]tg\alpha =\frac{sin\alpha }{cos\alpha }\\ \\\frac{sin\alpha }{cos\alpha } =-\frac{2}{9}\\ \\sin\alpha =-\frac{2}{9}cos\alpha \\ \\sin^{2} \alpha +cos^{2} \alpha =1\\\\(-\frac{2}{9}cos\alpha )^{2}+cos^{2}\alpha =1\\ \\ \frac{4}{81}cos^{2}\alpha +cos^{2}\alpha =1\\ \\ \frac{85}{81}cos^{2}\alpha =1\\ \\ cos^{2}\alpha =\frac{81}{85}\\ \\ cos\alpha =\frac{9\sqrt{85} }{85}\\ \\ lub\\ \\cos\alpha =-\frac{9\sqrt{85} }{85}[/tex]
[tex]sin\alpha =-\frac{2}{9}*(-\frac{9\sqrt{85} }{85})=\frac{2\sqrt{85} }{85}\\ \\ lub\\ \\sin\alpha =-\frac{2}{9}*\frac{9\sqrt{85} }{85}=-\frac{2\sqrt{85} }{85}[/tex]
[tex]ctg\alpha =\frac{1}{tg\alpha } =-\frac{9}{2}[/tex]
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Odpowiedź:
Szczegółowe wyjaśnienie:
[tex]tg\alpha =\frac{sin\alpha }{cos\alpha }\\ \\\frac{sin\alpha }{cos\alpha } =-\frac{2}{9}\\ \\sin\alpha =-\frac{2}{9}cos\alpha \\ \\sin^{2} \alpha +cos^{2} \alpha =1\\\\(-\frac{2}{9}cos\alpha )^{2}+cos^{2}\alpha =1\\ \\ \frac{4}{81}cos^{2}\alpha +cos^{2}\alpha =1\\ \\ \frac{85}{81}cos^{2}\alpha =1\\ \\ cos^{2}\alpha =\frac{81}{85}\\ \\ cos\alpha =\frac{9\sqrt{85} }{85}\\ \\ lub\\ \\cos\alpha =-\frac{9\sqrt{85} }{85}[/tex]
[tex]sin\alpha =-\frac{2}{9}*(-\frac{9\sqrt{85} }{85})=\frac{2\sqrt{85} }{85}\\ \\ lub\\ \\sin\alpha =-\frac{2}{9}*\frac{9\sqrt{85} }{85}=-\frac{2\sqrt{85} }{85}[/tex]
[tex]ctg\alpha =\frac{1}{tg\alpha } =-\frac{9}{2}[/tex]