Question

Найдите значение выражения √2/10 sin a+2, если cos a =√2/2, a∈ [180° ; 360°]

Answer 1

$\displaystyle\bf\\\alpha \in[180^\circ \ ; \ 360^\circ] \ \ \ \Rightarrow \ \ \ Sin\alpha < 0\\\\\\Sin\alpha =-\sqrt{1-Cos^{2}\alpha } =-\sqrt{1-\Big(\frac{\sqrt{2} }{2} \Big)^{2} }=-\sqrt{1-\frac{2}{4} } =\\\\\\=-\sqrt{1-\frac{1}{2} } =-\sqrt{\frac{1}{2} } =-\frac{1}{\sqrt{2} } \\\\\\\frac{\sqrt{2} }{10} Sin\alpha +2=\frac{\sqrt{2} }{10} \cdot\Big(-\frac{1}{\sqrt{2} } \Big)+2=-\frac{1}{10} +2=2-0,1=1,9\\\\\\Otvet \ : \ 1,9$