`1.`
`sin2x=-1/2`
`<=>sin2x=sin(-pi/6)`
`<=>`\(\left[ \begin{array}{l}2x=-\dfrac{\pi}{6}+k2\pi\\2x=\pi+\dfrac{\pi}{6}+k2\pi\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-\dfrac{\pi}{12}+k\pi\\2x=\dfrac{7\pi}{6}+k2\pi\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-\dfrac{\pi}{12}+k\pi\\x=\dfrac{7\pi}{12}+k\pi\end{array} \right.\)`(kinZZ)`
`2.`
`sin(x+45^o)=sqrt3/2`
`<=>``sin(x+45^o)=sin(60^o)`
`<=>`\(\left[ \begin{array}{l}x+45^o=60^o+k360^o\\x+45^o=180^o-60^o+k360^o\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=15^o+k360^o\\x=75^o+k360^o\end{array} \right.\)`(kinZZ)`
`3.`
`sin(pi/2-x)=1/3`
`<=>`\(\left[ \begin{array}{l}\dfrac{\pi}{2}-x=\arcsin\dfrac{1}{3}+k2\pi\\\dfrac{\pi}{2}-x=\pi-\arcsin\dfrac{1}{3}+k2\pi\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}-x=-\dfrac{\pi}{2}+\arcsin\dfrac{1}{3}+k2\pi\\-x=\dfrac{\pi}{2}-\arcsin\dfrac{1}{3}+k2\pi\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{\pi}{2}-\arcsin\dfrac{1}{3}-k2\pi\\x=-\dfrac{\pi}{2}+\arcsin\dfrac{1}{3}-k2\pi\end{array} \right.\)`(kinZZ)`
`4.`
`sin((2pi)/3-x)=0`
`<=>(2pi)/3-x=kpi`
`<=>-x=-(2pi)/3+kpi`
`<=>x=(2pi)/3-kpi(kinZZ)`
`5.`
`sin(pi/4-x)=sin2x`
`<=>`\(\left[ \begin{array}{l}\dfrac{\pi}{4}-x=2x+k2\pi\\\dfrac{\pi}{4}-x=\pi-2x+k2\pi\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}-3x=-\dfrac{\pi}{4}+k2\pi\\x=\dfrac{3\pi}{4}+k2\pi\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{\pi}{12}-\dfrac{k2\pi}{3}\\x=\dfrac{3\pi}{4}+k2\pi\end{array} \right.\)`(kinZZ)`
