求f(x)=2sin^2*x+2sinx*cosx-1的周期

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/16 19:01:39
求f(x)=2sin^2*x+2sinx*cosx-1的周期求f(x)=2sin^2*x+2sinx*cosx-1的周期求f(x)=2sin^2*x+2sinx*cosx-1的周期f(x)=2sin&

求f(x)=2sin^2*x+2sinx*cosx-1的周期
求f(x)=2sin^2*x+2sinx*cosx-1的周期

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

先利用倍角公式化简再做就行了