Question

Найти sin β, если ctg β=√8,a cos β=√8/2

Answer 1

$Ctg\beta =\sqrt{8}=\sqrt{4*2}=2\sqrt{2}\\\\Cos\beta=\frac{\sqrt{8} }{2}=\frac{2\sqrt{2}}{2}=\sqrt{2}\\\\Ctg\beta =\frac{Cos\beta }{Sin\beta}\\\\Sin\beta=\frac{Cos\beta }{Ctg\beta}=\frac{\sqrt{2}}{2\sqrt{2}}=\frac{1}{2}=0,5\\\\Otvet:\boxed{Sin\beta=0,5}$