已知函数f(x)=(1+cos2x)sin²x,x∈R,若f(a)=1/4,则f(a+π/8)=?
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/05 00:04:03
已知函数f(x)=(1+cos2x)sin²x,x∈R,若f(a)=1/4,则f(a+π/8)=?
f(x)=(1+cos2x)sin²x
=2cos²xsin²x=(1/2)(sin2x)²
f(a)=1/4
f(a)=(1/2)(sin2a)²=1/4
(sin2a)²=1/2
(cos2a)²=1/2
f(a+π/8)
=(1/2)[sin(2a+π/4)]²
=(1/2)[(√2/2)(sin2a+cos2a)]²
=(1/4)[1+2sin2acos2a]
=(1/4)[1+1]
=1/2
或
=(1/4)[1-1]
=0
=2cos²xsin²x=(1/2)(sin2x)²
f(a)=1/4
f(a)=(1/2)(sin2a)²=1/4
(sin2a)²=1/2
(cos2a)²=1/2
f(a+π/8)
=(1/2)[sin(2a+π/4)]²
=(1/2)[(√2/2)(sin2a+cos2a)]²
=(1/4)[1+2sin2acos2a]
=(1/4)[1+1]
=1/2
或
=(1/4)[1-1]
=0
已知函数f(x)=(1+cos2x)sin²x,x∈R,若f(a)=1/4,则f(a+π/8)=?
已知函数f(x)=(1+cos2x)sin^3x,x∈R,则f(x)是( )
已知函数f(x)=(1+cos2x)sin∧2x,x∈R,则f(x)是
已知函数f(x)=2sin²(π/4+x)-(√2)cos2x-1,x∈R 1.求f(x)最小值
已知函数f(x)=sin(2x+π/6)+sin(2x-π/6)+cos2x+a(a∈R,a为常数)
已知函数f(x)=sin(2x+π3)+sin(2x-π3)+2cos2x-1,x∈R.
已知函数f(x)=5sin(2x+φ),若对任意x ∈R,都有f(a+x)=f(a-x),则f(a+ π/4)=?
已知f(x)=sin(x+π/6)+sin(x-π/6)+acosx+b,(a,b∈R,且均为常数).(1)求函数f(x
已知函数f(x)=asinx-cos2x+a-3a+1,a∈R,a≠0.
已知函数f(x)=sin(2x+π6)+2sin2(x+π6)−2cos2x+a−1(a∈R,a为常数)
已知函数f(x)=2cos2x+3sin2x+a(a∈R).
已知函数f(x)=sin(2x+pai/6)+sin(2x-pai/6)+cos2x+a(a属于R,a为常数)