已知函数f(x)=sin^2x+根号3sinx×sin(x+π/2)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/13 11:24:06
已知函数f(x)=sin^2x+根号3sinx×sin(x+π/2)
(1)f(x)的最小正周期
(2)求f(x)的单调递增区间
(3)求f(x)在区间【0,2π/3】的取值范围
(1)f(x)的最小正周期
(2)求f(x)的单调递增区间
(3)求f(x)在区间【0,2π/3】的取值范围
“数理答疑团”为您解答,希望对你有所帮助.
(1)f(x)的最小正周期 π
f(x)=sin^2x+√3sinx×sin(x+π/2)
=(1-cos2x)/2 -√3sinxcosx
=1/2 -(cos2x)/2 -√3/2 sin2x
=1/2 -sin(2x+π/6)
(2)求f(x)的单调递增区间:[kπ+π/6,kπ+2π/3]
2kπ+π/2≤2x+π/6≤2kπ+3π/2 得:kπ+π/6≤x≤kπ+2π/3
(3)求f(x)在区间【0,2π/3】的取值范围
f(x)在区间【0,π/6】单调递减,取值范围:[-1/2,0]
f(x)在区间【π/6,2π/3】单调递增,取值范围:[-1/2,3/2]
所以:f(x)在区间【0,2π/3】的取值范围:[-1/2,3/2]
手机提问的朋友在客户端右上角评价点【满意】即可.
(1)f(x)的最小正周期 π
f(x)=sin^2x+√3sinx×sin(x+π/2)
=(1-cos2x)/2 -√3sinxcosx
=1/2 -(cos2x)/2 -√3/2 sin2x
=1/2 -sin(2x+π/6)
(2)求f(x)的单调递增区间:[kπ+π/6,kπ+2π/3]
2kπ+π/2≤2x+π/6≤2kπ+3π/2 得:kπ+π/6≤x≤kπ+2π/3
(3)求f(x)在区间【0,2π/3】的取值范围
f(x)在区间【0,π/6】单调递减,取值范围:[-1/2,0]
f(x)在区间【π/6,2π/3】单调递增,取值范围:[-1/2,3/2]
所以:f(x)在区间【0,2π/3】的取值范围:[-1/2,3/2]
手机提问的朋友在客户端右上角评价点【满意】即可.
已知函数f(x)=2cosx*sin(x+π/3)-根号3sin^2x+sinx*cosx
已知函数f(x)=[2sin(x+π/3)+sinx]cosx-根号3sin^2x,x属于R,求函数f(x)最小正周期
已知函数f(x)=sin(π/2-x)+sinx
已知函数f(x)=sinx+sin(x+π/2) ,
已知函数f(x)=(2sin(x+派/3)+sinx)cosx-根号3sin^2x,若存在
已知函数f(x)=sin平方x+根号3 sinx乘sin(x+派除以2) 求:
已知函数f(x)=[(2根号3sin^2x-sin2x)*cosx/sinx]+1
已知函数f(x)=2根号3sin平方x-sin(2x-π/3)
已知函数f(x)=2sinx*sin(π/2+x)-2sin^2x+1
已知函数f(x)=2cos(X)sin(X+π/3)-(根号3)(SINX)平方+sinXcosX
已知函数f(x)=2sinx*cos(1.5π+x)+(根号3下)*cosx*sin(π+x)+sin(0.5π+x)*
已知函数f(x)=[2sin(x+π/3)+sinx]cosx-√3sin²x,x∈R