[latex]sin frac{ pi*(2x-8)}{4} = frac{ sqrt{2}}{2} [/latex]

[latex]sin dfrac{ pi(2x-8)}{4} = dfrac{ sqrt{2}}{2} \ dfrac{ pi(2x-8)}{4}=dfrac{pi}{4}+2kpi vee dfrac{ pi(2x-8)}{4}=dfrac{3pi}{4}+2kpi\ pi(2x-8)=pi+8kpi vee pi(2x-8)=3pi+8kpi\ 2x-8=1+8k vee 2x-8=3+8k\ 2x=9+8k vee 2x=11+8k\ oxed{x=dfrac{4}{5}+4k vee x=dfrac{11}{2}+4k, (kinmathbb{Z})} [/latex]