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.

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

ответы:

$sin\alpha = -\frac{\sqrt5}5\\cos\alpha = -\frac{2\sqrt5}5\\ctg\alpha = \frac12$