Solve the equation sin x= root of 2 divided by 2

Solve the equation sin x= root of 2 divided by 2
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soyafh
$\mathrm{sin}x=\sqrt{2}/2$
$x=\left(-1{\right)}^{n}\ast \mathrm{arcsin}\left(\sqrt{2}/2\right)+\pi n,n\in Z$
$x=\left(-1{\right)}^{n}\ast \pi /4+\pi n,n\in Z$

Theodore Dyer
$\mathrm{sin}2x$ = (root of 2): 2 2x = (-1) to the power of n $\mathrm{arcsin}$ ((root of 2): 2) + $\mathrm{\Pi }$ * n, where n belongs to Z 2x = (-1) to the power of n $\mathrm{\Pi }$ / 4 + $\mathrm{\Pi }$*n, where n belongs to Z x = (-1) to the power of n $\mathrm{\Pi }$/4 :2 + ($\mathrm{\Pi }$*n) : 2 ... x = (-1) to the power of n $\mathrm{\Pi }$/8 + $\mathrm{\Pi }$/2 *n....