作业帮急求一道三角函数题解题过程.已知f(x)=2cos方ωx+2√3sinωxcosωx+a(ω>0,a∈R,a为常数),且满足条件f(x1)=f(x2)=0的|x1-x2|的最小值为π/2(1)求ω的值(2)若f(x)=[-π/6,π/3]上的最大值与最小值之和为3,求a的值
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/28 03:29:18
![急求一道三角函数题解题过程.已知f(x)=2cos方ωx+2√3sinωxcosωx+a(ω>0,a∈R,a为常数),且满足条件f(x1)=f(x2)=0的|x1-x2|的最小值为π/2(1)求ω的值(2)若f(x)=[-π/6,π/3]上的最大值与最小值之和为3,求a的值](/uploads/image/z/13328936-8-6.jpg?t=%E6%80%A5%E6%B1%82%E4%B8%80%E9%81%93%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E9%A2%98%E8%A7%A3%E9%A2%98%E8%BF%87%E7%A8%8B.%E5%B7%B2%E7%9F%A5f%28x%29%3D2cos%E6%96%B9%CF%89x%2B2%E2%88%9A3sin%CF%89xcos%CF%89x%2Ba%28%CF%89%3E0%2Ca%E2%88%88R%2Ca%E4%B8%BA%E5%B8%B8%E6%95%B0%29%2C%E4%B8%94%E6%BB%A1%E8%B6%B3%E6%9D%A1%E4%BB%B6f%28x1%29%3Df%28x2%29%3D0%E7%9A%84%7Cx1-x2%7C%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BA%CF%80%2F2%281%29%E6%B1%82%CF%89%E7%9A%84%E5%80%BC%282%29%E8%8B%A5f%28x%29%3D%5B-%CF%80%2F6%2C%CF%80%2F3%5D%E4%B8%8A%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%8E%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B9%8B%E5%92%8C%E4%B8%BA3%2C%E6%B1%82a%E7%9A%84%E5%80%BC)
急求一道三角函数题解题过程.已知f(x)=2cos方ωx+2√3sinωxcosωx+a(ω>0,a∈R,a为常数),且满足条件f(x1)=f(x2)=0的|x1-x2|的最小值为π/2(1)求ω的值(2)若f(x)=[-π/6,π/3]上的最大值与最小值之和为3,求a的值
急求一道三角函数题解题过程.
已知f(x)=2cos方ωx+2√3sinωxcosωx+a(ω>0,a∈R,a为常数),且满足条件f(x1)=f(x2)=0的|x1-x2|的最小值为π/2
(1)求ω的值
(2)若f(x)=[-π/6,π/3]上的最大值与最小值之和为3,求a的值
急求一道三角函数题解题过程.已知f(x)=2cos方ωx+2√3sinωxcosωx+a(ω>0,a∈R,a为常数),且满足条件f(x1)=f(x2)=0的|x1-x2|的最小值为π/2(1)求ω的值(2)若f(x)=[-π/6,π/3]上的最大值与最小值之和为3,求a的值
(1)f(x)=2cos²(ωx)+2√3sinωxcosωx+a
=sin²(ωx）+cos²(ωx)+cos²(ωx)-sin²(ωx）+2√3sinωxcosωx+a
=1+cos(2ωx)+√3sin(2ωx)+a
=2[sin(π/6)cos(2ωx)+cos(π/6)sin(2ωx)]+a+1
=2sin(π/6+2ωx)+a+1,
f(x1)=2sin(π/6+2ωx1)+a+1=0,f(x2)=2sin(π/6+2ωx2)+a+1=0,
sin(π/6+2ωx1)=sin(π/6+2ωx2)
2ωx1=2kπ+2ωx2, ω(x1-x2)=kπ x1-x2|=|kπ/ω|,
因其最小值为π/2,取k=1或k= -1,则ω=2.
(2)f(x)=2sin(π/6+4x)+a+1.
f(x)在区间[-π/6,π/3]上的最大值为a+3,最小值为a-1.
a+3+a-1=3,a=1/2.