[tex]c) \\\\P(-5; 12) \\|OP|=r\\r=\sqrt{(0+5)^2+(0-12)^2}=\sqrt{5^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}=13\\\\sin\alpha=\frac{y}r=\frac{12}{13}\\\\cos\alpha=\frac{x}r=\frac{-5}{13}=-\frac{5}{13}\\\\tg\alpha=\frac{y}x=\frac{12}{-5}=-2\frac25\\\\ctg\alpha=\frac{x}y=\frac{-5}{12}=-\frac5{12}[/tex]
[tex]d) \\P(-5, 10)\\r=\sqrt{(0+5)^2+(0-10)^2}=\sqrt{5^2+(-10)^2}=\sqrt{25+100}=\sqrt{125}=5\sqrt5\\\\sin\alpha=\frac{10}{5\sqrt5}*\frac{\sqrt5}{\sqrt5}=\frac{10\sqrt5}{5*5}=\frac{2\sqrt5}5\\\\cos\alpha=\frac{-5}{5\sqrt5}=-\frac{1}{\sqrt5}=-\frac{\sqrt5}5\\\\tg\alpha=\frac{10}{-5}=-2\\\\ctg\alpha=\frac{-5}{10}=-\frac12[/tex]
[tex]e)\\P(\sqrt5, 2)\\r=\sqrt{(0-\sqrt5)^2+(0-2)^2}=\sqrt{(-\sqrt5)^2+(-2)^2}=\sqrt{5+4}=\sqrt9=3\\\\sin\alpha=\frac{2}{3}\\\\cos\alpha=\frac{\sqrt5}3\\\\tg\alpha=\frac{2}{\sqrt5}=\frac{2\sqrt5}5\\\\ctg\alpha=\frac{\sqrt5}2[/tex]
[tex]f)\\P(\sqrt2, 1)\\r=\sqrt{(0-\sqrt2)^2+(0-1)^2}=\sqrt{(-\sqrt2)^2+(-1)^2}=\sqrt{2+1}=\sqrt3\\\\sin\alpha=\frac{1}{\sqrt3}=\frac{\sqrt3}3\\\\cos\alpha=\frac{\sqrt2}{\sqrt3}=\frac{\sqrt6}3\\\\tg\alpha=\frac{1}{\sqrt2}=\frac{\sqrt2}2\\\\ctg\alpha=\frac{\sqrt2}1=\sqrt2[/tex]
[tex]g) \\P(-\sqrt3, 1)\\r=\sqrt{(0+\sqrt3)^2+(0-1)^2}=\sqrt{(\sqrt3)^2+(-1)^2}=\sqrt{3+1}=\sqrt4=2\\\\sin\alpha=\frac{1}2\\\\cos\alpha=\frac{-\sqrt3}2=-\frac{\sqrt3}2\\\\tg\alpha=\frac{1}{-\sqrt3}=-\frac{\sqrt3}3\\\\ctg\alpha=\frac{-\sqrt3}1=-\sqrt3[/tex]
[tex]h)\\P(-\sqrt3, \sqrt6)\\r=\sqrt{(0+\sqrt3)^2+(0-\sqrt6)^2}=\sqrt{(\sqrt3)^2+(-\sqrt6)^2}=\sqrt{3+6}=\sqrt9=3\\\\sin\alpha=\frac{\sqrt6}3\\\\cos\alpha=\frac{-\sqrt3}3=-\frac{\sqrt3}3\\\\tg\alpha=\frac{\sqrt6}{-\sqrt3}=-\sqrt{\frac63}=-\sqrt2\\\\ctg\alpha=\frac{-\sqrt3}{\sqrt6}=-\frac{\sqrt{18}}6=-\frac{3\sqrt2}6=-\frac{\sqrt2}2[/tex]
