Question

Найдите sin a, если sin a * ctg a =
1/3. и 3пи/2<а<2пи

Answer 1

Ответ:

$\displaystye -\frac{2\sqrt2}{3}$

Объяснение:

$\displaystye sin a\cdot ctg a =\frac{1}{3}\\\\ sin a\cdot \frac{cos a}{sin a} =\frac{1}{3}\\\\cos a =\frac{1}{3}\\\\sin a=-\sqrt{1-cos^2 a}=-\sqrt{1-(\frac{1}{3})^2}=-\sqrt{1-\frac{1}{9}}=-\sqrt{\frac{8}{9}}=\\\\-\frac{\sqrt 8}{3}=-\frac{2\sqrt2}{3}$