Question

ctg=-4/3
270°<a<360°
найдите sin(270°+a)

Answer 1

$Sin(270 ^{o} + alpha ) = - Cos alpha$
$tg alpha *ctg alpha = 1$
$tg alpha = frac{1}{ctg alpha }= - frac{1}{ frac{4}{3} } =- frac{3}{4}$
$tg ^{2} alpha +1= frac{1}{Cos ^{2} alpha }$
$Cos ^{2} alpha = frac{1}{tg ^{2} alpha +1 }= frac{1}{(- frac{3}{4} ) ^{2}+1 } = frac{1}{ frac{9}{16}+1 }= frac{1}{ frac{25}{16} } = frac{16}{25}$
Так как α - угол четвёртой четверти, то $Cos alpha textgreater 0$
$Cos alpha = sqrt{ frac{16}{25} }= frac{4}{5}$
Тогда
$Sin(270 ^{o}+ alpha ) = - Cos alpha = - frac{4}{5}= - 0,8$