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[tex]sin\alpha=\frac{2}{7}\\\\\\Obliczam\ \ cos\alpha\\\\sin^2\alpha+cos^{2}\alpha=1\\\\(\frac{2}{7})^2+cos^2\alpha=1\\\\\frac{4}{49}+cos^2\alpha=1\\\\cos^2\alpha=1-\frac{4}{49}\\\\cos^2\alpha=\frac{49}{49}-\frac{4}{49}\\\\cos^2\alpha=\frac{45}{49}\\\\cos\alpha=\sqrt{\frac{45}{49}}\ \ \ \ \vee\ \ \ \ cos\alpha=-\sqrt{\frac{45}{49}}\\\\cos\alpha=\frac{\sqrt{45}}{\sqrt{49}}\ \ \ \ \vee\ \ \ \ cos\alpha=-\frac{\sqrt{45}}{\sqrt{49}}[/tex]
[tex]cos\alpha=\frac{\sqrt{9\cdot5}}{7}\ \ \ \ \vee\ \ \ \ cos\alpha=-\frac{\sqrt{9\cdot5}}{7}\\\\cos\alpha=\frac{3\sqrt{5}}{7}\ \ \ \ \vee\ \ \ \ cos\alpha=-\frac{3\sqrt{5}}{7}[/tex]
[tex]Obliczam\ \ tg\alpha\\\\tg\alpha=\frac{sin\alpha}{cos\alpha}\\\\tg\alpha=\dfrac{\frac{2}{7}}{\frac{3\sqrt{5}}{7}}\ \ \ \ \vee\ \ \ \ tg\alpha=\dfrac{\frac{2}{7}}{-\frac{3\sqrt{5} }{7}}\\\\tg\alpha=\frac{2}{7}:\frac{3\sqrt{5}}{7}\ \ \ \ \vee\ \ \ \ tg\alpha=\frac{2}{7}:(-\frac{3\sqrt{5}}{7})\\\\tg\alpha=\frac{2}{\not7}\cdot\frac{\not7}{3\sqrt{5}}\ \ \ \ \vee\ \ \ \ tg\alpha=-\frac{2}{\not7}\cdot\frac{\not7}{3\sqrt{5}}[/tex]
[tex]tg\alpha=\frac{2}{3\sqrt{5}}\ \ \ \ \ \ \vee\ \ \ \ tg\alpha=-\frac{2}{3\sqrt{5}}\\\\tg\alpha=\frac{2}{3\sqrt{5}}\cdot\frac{\sqrt{5}}{\sqrt{5}}\ \ \ \ \vee\ \ \ \ tg\alpha=-\frac{2}{3\sqrt{5}}\cdot\frac{\sqrt{5}}{\sqrt{5}}\\\\tg\alpha=\frac{2\sqrt{5}}{3\cdot5}\ \ \ \ \ \ \ \ \vee\ \ \ \ tg\alpha=-\frac{2\sqrt{5}}{3\cdot5}\\\\tg\alpha=\frac{2\sqrt{5} }{15}\ \ \ \ \ \ \ \ \vee\ \ \ \ tg\alpha=-\frac{2\sqrt{5}}{15}[/tex]
