Question

помогите пожалуйста
найдите 8 sin a если tg a = 0,75 и -П < a < -П/2

Answer 1

$8sin alpha - ?, -pi textless alpha textless -frac{pi}{2},\tg alpha =0,75.\\1+ctg^2 alpha =frac{1}{sin^2 alpha },\\sin^2 alpha =frac{1}{1+ctg^2 alpha },\\sin^2 alpha =frac{1}{1+frac{1}{tg^2 alpha }},\\sin alpha =pmsqrt{frac{1}{1+frac{1}{tg^2 alpha }}},\\-pi textless alpha textless -frac{pi}{2} to sin alpha =-sqrt{frac{1}{1+frac{1}{tg^2 alpha }}},\\sin alpha =-sqrt{frac{1}{1+frac{1}{0,75^2}}}=-sqrt{0,36}=-sqrt{0,6^2}=-0,6;\\8sin alpha =8cdot (-0,6)=-4,8.\\OTBET: 8sin alpha=-4,8$