oblicz wartości pozostałych funkcji trygonometrycznych kąta ostrego alfa jeśli .
a) sin alfa = 1/10
b) tg alfa = pierwiastek z 5
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sin²a+cos²a=1
a) sin a = 1/10
(1/10)²+cos²a=1
1/100+cos²a=1
cos²a= 99/100
cos a=![\frac{3\sqrt{11}}{10} \\ tg\alpha= \frac{sin\alpha}{cos\alpha}\\ tg\alpha=\frac{\frac{1}{10}}{\frac{3\sqrt{11}}{10}}\\ tg\alpha= \frac{1}{3\sqrt{11}}\\ tg\alpha= \frac{3\sqrt{11}}{99}\\ tg\alpha= \frac{\sqrt{11}}{33}\\ ctg\alpha= \frac{cos\alpha}{sin\alpha}\\ ctg\alpha= \frac{\frac{3\sqrt{11}}{10}}{\frac{1}{10}} \\ ctg\alpha= 3\sqrt{11} \frac{3\sqrt{11}}{10} \\ tg\alpha= \frac{sin\alpha}{cos\alpha}\\ tg\alpha=\frac{\frac{1}{10}}{\frac{3\sqrt{11}}{10}}\\ tg\alpha= \frac{1}{3\sqrt{11}}\\ tg\alpha= \frac{3\sqrt{11}}{99}\\ tg\alpha= \frac{\sqrt{11}}{33}\\ ctg\alpha= \frac{cos\alpha}{sin\alpha}\\ ctg\alpha= \frac{\frac{3\sqrt{11}}{10}}{\frac{1}{10}} \\ ctg\alpha= 3\sqrt{11}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5Csqrt%7B11%7D%7D%7B10%7D+%5C%5C%C2%A0tg%5Calpha%3D+%5Cfrac%7Bsin%5Calpha%7D%7Bcos%5Calpha%7D%5C%5C+tg%5Calpha%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B10%7D%7D%7B%5Cfrac%7B3%5Csqrt%7B11%7D%7D%7B10%7D%7D%5C%5C+tg%5Calpha%3D+%5Cfrac%7B1%7D%7B3%5Csqrt%7B11%7D%7D%5C%5C+tg%5Calpha%3D+%5Cfrac%7B3%5Csqrt%7B11%7D%7D%7B99%7D%5C%5C+tg%5Calpha%3D+%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B33%7D%5C%5C+ctg%5Calpha%3D+%5Cfrac%7Bcos%5Calpha%7D%7Bsin%5Calpha%7D%5C%5C+ctg%5Calpha%3D+%5Cfrac%7B%5Cfrac%7B3%5Csqrt%7B11%7D%7D%7B10%7D%7D%7B%5Cfrac%7B1%7D%7B10%7D%7D+%5C%5C+ctg%5Calpha%3D+3%5Csqrt%7B11%7D)
b)![tg\alha= \sqrt{5}\\ tg\alpha*ctg\alpha=1\\ \sqrt{5}*ctg\alpha=1\\ ctg\alpha= \frac{1}{\sqrt{5}}\\ ctg\alpha= \frac{\sqrt{5}}{5}\\ tg\alpha= \frac{sin\alpha}{cos\alpha}\\ \sqrt{5}= \frac{sin\alpha}{cos\alpha}\\ \sqrt{5}cos\alpha= sin\alpha\\ sin^\alpha+cos^2\alpha=1\\ (\sqrt{5}cos\alpha)^2+cos^2\alpha=1 \\ 5cos^2\alpha+cos^2\alpha=1\\ 6cos^2\alpha= 1\\ cos^2\alpha= \frac{1}{6}\\ cos\alpha= \frac{\sqrt{6}}{6}\\ sin\alpha= \sqrt{5}*\frac{\sqrt{6}}{6}\\ sin\alpha= \frac{\sqrt{30}}{6}\\ Licze \ na \ naj \ :) tg\alha= \sqrt{5}\\ tg\alpha*ctg\alpha=1\\ \sqrt{5}*ctg\alpha=1\\ ctg\alpha= \frac{1}{\sqrt{5}}\\ ctg\alpha= \frac{\sqrt{5}}{5}\\ tg\alpha= \frac{sin\alpha}{cos\alpha}\\ \sqrt{5}= \frac{sin\alpha}{cos\alpha}\\ \sqrt{5}cos\alpha= sin\alpha\\ sin^\alpha+cos^2\alpha=1\\ (\sqrt{5}cos\alpha)^2+cos^2\alpha=1 \\ 5cos^2\alpha+cos^2\alpha=1\\ 6cos^2\alpha= 1\\ cos^2\alpha= \frac{1}{6}\\ cos\alpha= \frac{\sqrt{6}}{6}\\ sin\alpha= \sqrt{5}*\frac{\sqrt{6}}{6}\\ sin\alpha= \frac{\sqrt{30}}{6}\\ Licze \ na \ naj \ :)](https://tex.z-dn.net/?f=tg%5Calha%3D+%5Csqrt%7B5%7D%5C%5C+tg%5Calpha%2Actg%5Calpha%3D1%5C%5C+%5Csqrt%7B5%7D%2Actg%5Calpha%3D1%5C%5C+ctg%5Calpha%3D+%5Cfrac%7B1%7D%7B%5Csqrt%7B5%7D%7D%5C%5C+ctg%5Calpha%3D+%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B5%7D%5C%5C+tg%5Calpha%3D+%5Cfrac%7Bsin%5Calpha%7D%7Bcos%5Calpha%7D%5C%5C+%5Csqrt%7B5%7D%3D+%5Cfrac%7Bsin%5Calpha%7D%7Bcos%5Calpha%7D%5C%5C+%5Csqrt%7B5%7Dcos%5Calpha%3D+sin%5Calpha%5C%5C+sin%5E%5Calpha%2Bcos%5E2%5Calpha%3D1%5C%5C+%28%5Csqrt%7B5%7Dcos%5Calpha%29%5E2%2Bcos%5E2%5Calpha%3D1+%5C%5C+5cos%5E2%5Calpha%2Bcos%5E2%5Calpha%3D1%5C%5C+6cos%5E2%5Calpha%3D+1%5C%5C+cos%5E2%5Calpha%3D+%5Cfrac%7B1%7D%7B6%7D%5C%5C+cos%5Calpha%3D+%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B6%7D%5C%5C+sin%5Calpha%3D+%5Csqrt%7B5%7D%2A%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B6%7D%5C%5C+sin%5Calpha%3D+%5Cfrac%7B%5Csqrt%7B30%7D%7D%7B6%7D%5C%5C+Licze+%5C+na+%5C+naj+%5C+%3A%29)