Question

求解：已知x=π/4是f(x)=asinx+bcosx一条对称轴,且最大值为2√2,则函数g(x)=asinx+b为多少

Answer 1

f(x)=asinx+bcosx=√a²+b²sin(x+φ)

a²+b²=8

f(π/4)=√2/2(a+b)=-2√2 or 2√2,

a+b=-4 or 4

∴a=b=-2 or a=b=2

g(x)=2sinx+2 or g(x)=-2sinx-2