Question

已知函数y=f(x)=(sinx)平方-根号3sin(pai+x)*cosx

Answer 1

y=f(x)=(sinx)平方-根号3sin(pai+x)*cosx

=(1/2)(1-cos2x)+根号3sinxcosx

=(√3/2)sin2x-(1/2)cos2x+1/2

=sin(2x-π/6)+1/2

所以最小正周期T=2π/2=π

最大值=1+1/2=3/2

此时2x-π/6=2kπ+π/2

x=kπ+π/3 k∈Z