已知函数f(x)=2sin(x/4)cos(x/4)-2√3sin²(x/4)+√3,且g(x)=f(x+π/3)(1)判断g(x)的奇偶性 (2)求g(x)的单调递增区间
来源:学生作业帮助网 编辑:作业帮 时间:2024/05/14 11:47:04
已知函数f(x)=2sin(x/4)cos(x/4)-2√3sin²(x/4)+√3,且g(x)=f(x+π/3)
(1)判断g(x)的奇偶性 (2)求g(x)的单调递增区间
f(x)=sin(x/2) -√3[1-cos(x/2)]+√3
=2[(1/2)sin(x/2) +(√3/2)cos(x/2)]
=2sin(x/2+π/3)
(1) g(x)=f(x+π/3)=2sin[(x+π/3)/2 +π/3)]=2sin(x/2 +π/2)=2cos(x/2)
所以 g(x)是偶函数.
(2)令 -π+2kπ≤x/2≤2kπ,得
-2π+4kπ≤x≤4kπ,
所以 增区间为
[-2π+4kπ,4kπ],k是整数.
1
f(x)=2sin(x/4)cos(x/4)-2√3sin²(x/4)+√3
f(x)=2sin(x/4)cos(x/4)-√3(-2sin²(x/4)+1)
=sin(x/2)-√3cos(x/2)
=2sin(x/2-π/3)
g(x)=2sin[(x+π/3)/2-π/3]
=2sin(x/2-π/6)
对称轴x...
全部展开
1
f(x)=2sin(x/4)cos(x/4)-2√3sin²(x/4)+√3
f(x)=2sin(x/4)cos(x/4)-√3(-2sin²(x/4)+1)
=sin(x/2)-√3cos(x/2)
=2sin(x/2-π/3)
g(x)=2sin[(x+π/3)/2-π/3]
=2sin(x/2-π/6)
对称轴x/2-π/6=kπ+π/2
x=2kπ+4π/3≠0
∴g(x)是非奇非偶函数
2
2kπ-π/2≤x/2-π/6≤2kπ+π/2
4kπ-2π/3≤x≤4kπ+4π/3
收起
已知函数f(x)=(1+1 anx)sin^2x+m sin(x+π/4)sin(x-π/4)
已知函数f(x)=cos2x/[sin(π/4-x)]
已知函数F(X)=SIN(2X+φ)(-π
已知函数f(x)=sin(2x+φ) (0
已知函数f(x)=4sinx-2/1+sin²x 证明f(x+2π)=f(x)
已知函数f(x)=2^(2-x),x>=2;f(x)=sinπx/4,-2
已知函数f(x)=2(sin^4 x+cos^4 x)+m(sin^x+cosx)^4在0=
已知函数f(x)=-3sin^2-4cosx+2 求f(x)最大最小值
已知函数f(x)=sin²(π/4+x)+cos²x+1/2求最值
已知函数f(x)=-1/2+sin(5/2x)/2sin(x/2)(0
已知函数f x=-2√3sin ²x+sin 2x+√3
已知函数f(x)=2根号3sin平方x-sin(2x-π/3)
已知函数f x=a(2sin ²x/2+sin x)+b
已知函数f(x)=sin(2x+π/2),设g(x)=f(x)+f(π/4-x),求函数g(x)的单调递增区间
已知函数f(x)=(6cos^4x+5sin^2x-4)/cos2x 判断f(x)的奇偶性
已知函数f(x)=cos^4x-2sinxcosx-sin^4x,求f(x)的值域
已知函数f(x)=loga(1+sin^2(x/2)-sin^4(x/2)),其中0
已知函数f(x)=2根号3sin(x/2+派/4)cos(x/2+派/4)-sin(x+派).求f(x)的最小正周期