Question

Найдите значение (тригонометрия)

Answer 1

$\displaystyle\bf\\Sinx=-\frac{1}{8} \\\\x\in\Big[-\frac{\pi }{2} \ ; \ 0\Big] \ \ \ \Rightarrow \ \ \ Cosx > 0\\\\\\Cosx=\sqrt{1-Sin^{2} x} =\sqrt{1-\Big(-\frac{1}{8} \Big)^{2} }=\sqrt{1-\frac{1}{64} } =\sqrt{\frac{63}{64} }=\\\\\\=\sqrt{\frac{9\cdot 7}{8^{2} } } =\frac{3\sqrt{7} }{8} \\\\\\Otvet \ : \ Cosx=\frac{3\sqrt{7} }{8}$