Question

8sin(5p/2+a) если sin a=-0,6 и a принадлежит (3p/2;2p)​

Answer 1

$\displaystyle\bf\\8Sin\Big(\frac{5\pi }{2} +\alpha \Big)=8Sin\Big[2\pi +\Big(\frac{\pi }{2} +\alpha \Big)\Big]=8Sin\Big(\frac{\pi }{2}+\alpha \Big)=8Cos\alpha \\\\\\\alpha \in\Big(\frac{3\pi }{2} \ ;\ 2\pi \Big) \ \ \ \Rightarrow \ \ \ Cos\alpha > 0\\\\\\8Cos\alpha =8\cdot\sqrt{1-Sin^{2} \alpha } =8\cdot\sqrt{1-(-0,6)^{2} } =8\cdot\sqrt{1-0,36} =\\\\\\8\cdot\sqrt{0,64} =8\cdot 0,8=6,4$