Question

已知函数f(x)=asinx+bcosx(1)当f(π/4)=√2,且f(x)的最大值为√10时,求a,b的值;(2

Answer 1

f(x)=√a^2+b^2(sin(x+d))

d=tan(b/a)

由题意知x+d=π/2时,d=π/4 ,a=b

a^2+b^2=10,a=b=√5