已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,-π/2

来源：学生作业帮助网编辑：六六作业网时间：2024/11/05 16:37:17

已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,-π/2已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,-π/2已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,-π

已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,-π/2
已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,-π/2

已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,-π/2
(1)
不妨取ωx₁+φ = -π/2,ωx₂+φ = π/2 (-π/2,π/2为相邻对称轴)
ωx₂+φ - (ωx₁+φ) = ω(x₂ - x₁) = ωπ/2 = π/2 - (-π/2) = π
ω = 2
最高点y = 4,A = 4
x = 5π/12,y取最大值,ω(5π/12) + φ = π/2,5π/6 + φ = π/2,φ = -π/3
f(x) = 4sin(2x - π/3)
f(x)周期为π
x = 5π/12 + nπ时,y取最大值
x = -π/12 + nπ时,y取最小值
x∈(-π/12 + nπ,5π/12 + nπ),单调增
x∈(5π/12 + nπ,11π/12 + nπ),单调减
(2)
5π/12在[π/4,π/2]内,函数f(x)的最大值=4
f(π/4) = 4sin(π/2 - π/3) = 4sin(π/6) = 2
f(π/2) = 4sin(π - π/3) = 2√3 > f(π/4)
最小值2

已知函数f（x）＝Asin(wx+φ)(A 已知函数f(x)=Asin(wx+φ)图像如图求f(x) 已知函数f(x)= Asin(wx+φ)(x属于R,A>0,w>0,|φ| 已知函数f(x)=Asin(wx+φ)(x∈R,A>0,w>0,0 已知函数f(x)=Asin(wx+φ)(x∈R,A>0,w>0,0 已知函数f（x）=Asin（wx+φ）)(A>0,w>0,|x| 已知函数f( x )=Asin (wx +φ)(x属于R,w>0,0 函数f(x)=Asin(wx+φ),A>0,|φ| 三角函数问题f(x)=Asin(wx+φ)+B已知函数f(x)=Asin(wx+φ) +B(A>0,w>o,|ф| 已知函数f(x)=Asin(wx+φ)+B(A>0,φ>1,|φ| 已知函数f(x)=Asin(wx+φ)(A>0,w>0,│φ│ 已知函数f[x]=asin[wx+φ][a>0,w>0,|φ| 已知函数f(x)=Asin(wx+φ)(A>0,w>0,│φ│ 【急!】已知函数f(x)=Asin(wx+ φ)(其中A>0,w>0,| φ| 已知函数f(x)=Asin(wx+φ)(A>0,w>0)|φ| 已知函数f(x)=Asin(wx+φ),(A>0,w>0,|φ| 已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ| 已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ|