Question

Решите уравнение срочно

Sin 2pi/x=√2/2

Answer 1

$sin \frac{2\pi}{x}= \frac{\sqrt2}{2}\\\frac{2\pi}{x}=(-1)^n \frac{\pi}{4}+\pi n,n\in z\\ x= \frac{2\pi}{(-1)^n \frac{\pi}{4}+\pi n,n\in z} \\x=(-1)^n2\pi*\frac{4}{\pi}+ \frac{2\pi}{\pi}n,n\in z\\x=(-1)^n8+2n,n\in z$

Answer 2

sin2π/x=√2/2
2π/x=π/4+2πk U 2π/x=3π/4+2πk
x=8+1/2k U x=8/3+1/2k,k∈z