Question

(1/2)已知函数f(x)=2acos^x+bsinxcosx-根号3/2,且f(0)=根号3/2,f(派/4)=1/2

Answer 1

(1)f(0)=a-√3/2=√3/2,a=√3

f(pi/4)=a/2+b/2-√3/2=1/2,b=1

f(x)=√3/2(1+cos2x)+1/2sin2x-√3/2=sin(2x+pi/3)

f(x)的最小正周期=2pi/2=pi

(2)令2x+pi/3=0,则x=-pi/6,f(x)图象向右平移pi/6成为奇函数.