Question

3)Для острого угла а, найдите cos a; tga; ctga, если ѕіn a = 8/16

Answer 1

$\displaystyle\bf\\Sin\alpha =\frac{8}{16}=\frac{1}{2} \\\\\\Cos\alpha =\sqrt{1-Sin^{2}\alpha } =\sqrt{1-\Big(\frac{1}{2}\Big)^{2} } =\sqrt{1-\frac{1}{4} } =\sqrt{\frac{3}{4} } =\frac{\sqrt{3} }{2} \\\\\\tg\alpha =\frac{Sin\alpha }{Cos\alpha } =\frac{1}{2} :\frac{\sqrt{3} }{2} =\frac{1}{2} \cdot\frac{2}{\sqrt{3} }=\frac{1}{\sqrt{3} } =\frac{\sqrt{3} }{3} \\\\\\Ctg\alpha =\frac{1}{tg\alpha } =1:\frac{1}{\sqrt{3} }=1\cdot\sqrt{3} =\sqrt{3}$

$\displaystyle\bf\\Otvet:Cos\alpha =\frac{\sqrt{3} }{2} \ \ ; \ \ tg\alpha =\frac{\sqrt{3} }{3} \ \ ; \ \ Ctg\alpha =\sqrt{3}$