Question

Arccos(sin 4П/5)=????????????

Answer 1

$arccos (sin\frac{4\pi}{5})=arccos(sin(\pi -\frac{\pi}{5}))=arccos (sin(\frac{\pi }{5}))=\\\\=arccos(sin(\underbrace {\frac{\pi }{2}-\frac{3\pi}{10}}_{\pi /5}))=arccos(cos\frac{3\pi}{10})=\frac{3\pi}{10}\; ;\\\\\frac{3\pi}{10}\in \; 1\; chetverti$