`1.`
`sinx = -(\sqrt{2})/2`
`sinx=sin(-π/4)`
`⇔` $\left[\begin{matrix} x=-\dfrac{π}{4}+k2π\\ x=π+\dfrac{π}{4}+k2π\end{matrix}\right.$
`⇔` $\left[\begin{matrix} x=-\dfrac{π}{4}+k2π\\ x=\dfrac{5π}{4}+k2π\end{matrix}\right.(k∈Z)$
`2.`
`sinx =1/(\sqrt{3})`
`⇔` $\left[\begin{matrix} x=arcsin\dfrac{1}{\sqrt{3}}+k2π\\ x=π-arcsin\dfrac{1}{\sqrt{3}}+k2π\end{matrix}\right.(k∈Z)$
`3.`
`sin2x =1`
`⇔2x=π/2+k2π`
`⇔x=π/4+kπ(k∈Z)`
`4.`
`sin(3x+π/4)=sin2x`
`⇔` $\left[\begin{matrix} 3x+\dfrac{π}{4}=2x+k2π\\ 3x+\dfrac{π}{4}=π-2x+k2π\end{matrix}\right.$
`⇔` $\left[\begin{matrix} 3x-2x=-\dfrac{π}{4}+k2π\\ 3x+2x=-\dfrac{π}{4}+π+k2π\end{matrix}\right.$
`⇔` $\left[\begin{matrix} x=-\dfrac{π}{4}+k2π\\ 5x=\dfrac{3π}{4}+k2π\end{matrix}\right.$
`⇔` $\left[\begin{matrix} x=-\dfrac{π}{4}+k2π\\ x=\dfrac{3π}{20}+k\dfrac{2π}{5}\end{matrix}\right.(k∈Z)$
