Question

найдите 5sin a,если

Answer 1

Ответ:   5sina=1 .

$cosa=-\dfrac{2\sqrt6}{5}\\\\\\a\in \Big(\dfrac{\pi}{2}\ ;\ \pi \Big)\ \ \ \Rightarrow \ \ \ sina>0\\\\\\\boxed{\ sin^2a+cos^2a=1\ \ \Rightarrow \ \ \ sin^2a=1-cos^2a\ \ ,\ \ sina=\pm \sqrt{1-cos^2a}\ }\\\\\\sina>0\ \ ,\ \ sina=+\sqrt{1-\dfrac{4\cdot 6}{25}}=\sqrt{\dfrac{25-14}{25}}=\dfrac{1}{5}\\\\5\, sina=5\cdot \dfrac{1}{5}=1$