Question

Решите уравнение sin (х + п/4) = корень 2/2 на промежутке (0; 2п).​

Answer 1

$sin(x+\frac{\pi }{4})=\frac{\sqrt2}{2}\\\\x+\frac{\pi}{4}=(-1)^{n}\cdot \frac{\pi}{4}+\pi n\; ,\; n\in Z\\\\x=-\frac{\pi}{4}+(-1)^{n}\cdot \frac{\pi}{4}+\pi n \; ,\; n\in Z\\\\ili\; \; \; \; x=\left [{-\frac{\pi}{4}+\frac{\pi}{4}+2\pi n=2\pi n\; ,\; n\in Z\quad } \atop {-\frac{\pi}{4}+\frac{3\pi }{4}+2\pi k=\frac{\pi}{2}+2\pi k\; ,\; k\in Z}} \right. \\\\x\in (0,2\pi )\, :\; \; x=\frac{\pi}{2}\; .$