Question

已知函数f(x)=asinx-bcosx(a,b为常数,a≠0,x∈R)在x=π/4处取得最小值,则函数y=f(3π/4

Answer 1

①cosφ=a/根号(a^2+b^2),sinφ=b/根号(a^2+b^2),=>tanφ=b/a

f(x)=asinx-bcosx=根号(a^2+b^2)(sinxcosφ-cosxsinφ)根号(a^2+b^2)sin(x-φ)

②f(x)=asinx-bcosx在x=π/4处取得最小值

=>sin(x-φ)在x=π/4处取得最小值

=>x-φ=π/4-φ=3π/2