(1)
∵当Asin(wx+π/4)=1时得最大值A
∴A=2
最小正周期=2π/w=8
w=π/4
f(x)=2sin(πx/4+π/4)
(2)
f(2)=2sin(π*2/4+π/4)=2sin(π/2+π/4)=2cosπ/4=√2
f(4)=2sin(π*4/4+π/4)=2sin(π+π/4)=-2sinπ/4=-√2
∴P点坐标是(2,√2) Q点坐标是(4,-√2)
则直线PQ的方程是
(x-2)/(4-2)=(y-√2)/(-√2-√2)
代简得
y=-√2x+3√2
此直线与X轴的交点坐标M是(3,0)
∴S△POQ=S△OPM+S△OQM
=1/2*|OM|*|py|+1/2*|OM|*|qy|
=1/2*|OM|*(|py|+|qy|)
=1/2*3*(√2+√2)
=3√2