Question

вычислите cos(π+a), если sina=-7/9 и а принадлежит (π;3π/2)​

Answer 1

$sin\alpha=-\frac{7}{9}; \pi <\alpha<\frac{3\pi }{2}\\cos(\pi+\alpha)=-cos\alpha\\cos\alpha = -\sqrt{1-sin^2\alpha}=-\sqrt{1-(-\frac{7}{9})^2}=-\sqrt{1-\frac{49}{81}}=-\sqrt {\frac{32}{81}}=-\frac{4\sqrt2}{9}\\cos(\pi+\alpha)=\frac{4\sqrt2}{9}$