Question

найдите sin a, cos a, tg a, если ctg a=2 и sin a меньше нуля

Answer 1

Если ctga > 0; sina < 0 ⇒ tga > 0; cosa < 0.

$ctgalpha = 2\frac{cosalpha}{sinalpha} = 2\cosalpha = 2*sinalpha\cos^2alpha = 4*sin^2alpha\1 - sin^2alpha = 4*sin^2alpha\5*sin^2alpha = 1\sin^2alpha = frac15\sinalpha = -frac{1}{sqrt5} = -frac{sqrt5}5\cos^2alpha = 4*frac5{25} = frac45\cosalpha = -frac2{sqrt5} = -frac{2sqrt5}5\tgalpha = frac1{ctgalpha} = frac12$

Ответы:

$sinalpha = -frac{sqrt5}5\cosalpha = -frac{2sqrt5}5\ctgalpha = frac12$