1. cosα= 0,8
[tex]x^{2}+8^{2}=10^{2} \\x^{2}+64=100\\ x^{2}=36\\ x=6[/tex]
[tex]sin\alpha=\frac{6}{10}=0,6\\ tg \alpha=\frac{6}{8}=0,75\\ ctg\alpha=\frac{8}{6}=1\frac{1}{3}[/tex]
2. sinα=0,4
[tex]x^{2}+4^{2}=10^{2}\\ x^{2}+16=100\\ x^{2}=84\\ x=\sqrt{84}=\sqrt{4 \cdot 21}=2\sqrt{21}[/tex]
[tex]cos\alpha=\frac{2\sqrt{21}}{10}=\frac{\sqrt{21}}{5}\\ tg\alpha=\frac{4}{2\sqrt{21}}=\frac{2}{\sqrt{21}}\cdot \frac{\sqrt{21}}{\sqrt{21}}=\frac{2\sqrt{21}}{21}\\ ctg\alpha=\frac{2\sqrt{21}}{4}=\frac{\sqrt{21}}{2}[/tex]
3. [tex]tg\alpha=2,4=\frac{12}{5}[/tex]
[tex]5^{2}+12^{2}=x^{2}\\ x^{2}=25+144\\ x^{2}=169\\ x=13[/tex]
[tex]sin\alpha=\frac{12}{13}\\ cos \alpha=\frac{5}{13}\\ ctg\alpha=\frac{5}{12}[/tex]
