Question

Вычислите sin 2a и cos 2a, если sin a = 3/5 и п/2<а<п

Answer 1

$\displaystyle sin2a=2sina*cosa\\\\cos2a=cos^2a-sin^2a=1-2sin^2a\\\\sina=\frac{3}{5}; a \in II; cosa<0\\\\cosa=-\sqrt{1-(\frac{3}{5})^2}=-\sqrt{1-\frac{9}{25}}=-\frac{4}{5}\\\\sin2a=2*\frac{3}{5}*(-\frac{4}{5})=-\frac{24}{25}=-0.96\\\\cos2a=1-2*\frac{9}{25}=\frac{7}{25}$