Question

Найдите значение sin(φ + 30°), если sin φ = $\frac{\sqrt{3}}{4}$ ,
90°<φ<180°

Answer 1

$sin\varphi =\frac{\sqrt3}{4}\\\\\varphi \in (90^\circ ,180^\circ )\; \; \Rightarrow \; \; cos\varphi \ \textless \ 0\; ,\\\\cos\varphi =-\sqrt{1-sin^2\varphi }=-\sqrt{1-\frac{3}{16}}=-\frac{\sqrt{13}}{4}\\\\sin(\varphi +30^\circ )=sin\varphi \cdot cos30^\circ +cos\varphi \cdot sin30^\circ=\\\\=\frac{\sqrt3}{4}\cdot \frac{\sqrt3}{2}-\frac{\sqrt{13}}{4}\cdot \frac{1}{2}=\frac{3-\sqrt{13}}{8}$