已知函数f(x)=(sinx+cosx)sinx, - 知识问答

已知函数f(x)=(sinx+cosx)sinx,x属于R,则f(x)的最小正周期T和最小值A分别是?

1个回答

f(x)=(sinx+cosx)sinx
=sin^2x+sinxcosx
=(1-cos2x)/2+1/2*sin2x
=1/2*sin2x-1/2*cos2x+1/2
=√2(√2/2*sin2x-√2/2*cos2x)+1/2
=√2(sin2xcosπ/4-cos2xsinπ/4)+1/2
=√2sin(2x-π/4)+1/2
T=2π/2=π
-1

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