Question

вызначте tga, когда cosa =-4/5 и пи/2 ​

Answer 1

$\displaystile\bf\\Cos\alpha =-\frac{4}{5} \ \ ;\ \ \frac{\pi }{2} <\alpha <\pi \\\\\\1+tg^{2} \alpha =\frac{1}{Cos^{2} \alpha } \\\\\\tg^{2} \alpha =\frac{1}{Cos^{2} \alpha } -1=\frac{1}{(-\frac{4}{5} )^{2} } -1=\frac{1}{\frac{16}{25} } -1=\frac{25}{16} -1=\frac{9}{16} \\\\\\tg\alpha =-\sqrt{\frac{9}{16} } =-\frac{3}{4}=-0,75\\\\\\Otvet:tg\alpha =-0,75$

Второй способ :

$\displaystyle\bf\\Sin\alpha =\sqrt{1-Cos^{2}\alpha } =\sqrt{1-\Big(-\frac{4}{5} \Big)^{2} } =\sqrt{1-\frac{16}{25} } =\sqrt{\frac{9}{25} } =\frac{3}{5} \\\\\\tg\alpha =\frac{Sin\alpha }{Cos\alpha } =\frac{3}{5} :\Big(-\frac{4}{5} \Big)=-\frac{3}{5} \cdot\frac{5}{4}=-\frac{3}{4} =-0,75$