t=(-1)^(k+1)π/4+πk, k ⊂ z
sinx=a ⇒ x=(-1)^(k) arcsina + πk, k ∈ Z
|a| ≤ 1
sint=[m]-\frac{\sqrt{2}}{2} [/m] ⇒ [m]x=(-1)^{k} arcsin(-\frac{\sqrt{2}}{2}) + πk, k \in Z[/m]
так как [m] arcsin(-\frac{\sqrt{2}}{2}) =-\frac{\pi}{4}[/m], то
[m]t=(-1)^{k} (-\frac{\pi}{4}) + πk, k \in Z[/m],
упростим:
[m]t=(-1)^{k+1} (\frac{\pi}{4}) + πk, k \in Z[/m]
О т в е т. [m](-1)^{k+1} (\frac{\pi}{4}) + πk, k \in Z[/m]