一道关于求三角函数周期题目
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/18 01:01:25
一道关于求三角函数周期题目
f(x)=5sinxcosx-5根号3(cosx)^2+(5根号3)/2
f(x)=5sinxcosx-5根号3(cosx)^2+(5根号3)/2
![一道关于求三角函数周期题目](/uploads/image/z/18959394-66-4.jpg?t=%E4%B8%80%E9%81%93%E5%85%B3%E4%BA%8E%E6%B1%82%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E5%91%A8%E6%9C%9F%E9%A2%98%E7%9B%AE)
f(x)=(5/2)*(2sinxcosx)-5√3*(cos2x+1)/2+5√3/2
=(5/2)sin2x-5√3cosx/2-5√3/2+5√3/2
=5[(1/2)sin2x-√3cos2x/2]
=5(sin2xcos(π/3)-cos2xsin(π/3)]
=5sin(2x-π/3)
所以T=2π/2=π
=(5/2)sin2x-5√3cosx/2-5√3/2+5√3/2
=5[(1/2)sin2x-√3cos2x/2]
=5(sin2xcos(π/3)-cos2xsin(π/3)]
=5sin(2x-π/3)
所以T=2π/2=π