已知函数f(x)=cos(2x-3.14/3)+2sin(x-3.14/4)sin(x+3.14/4)(1)求函数f(x)的最小正周期和图像的对称轴方程 (2)求函数f(x)在区间[-3.14/12,3.14/2]上的值域
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![已知函数f(x)=cos(2x-3.14/3)+2sin(x-3.14/4)sin(x+3.14/4)(1)求函数f(x)的最小正周期和图像的对称轴方程 (2)求函数f(x)在区间[-3.14/12,3.14/2]上的值域](/uploads/image/z/1168722-18-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dcos%282x-3.14%2F3%29%2B2sin%28x-3.14%2F4%29sin%28x%2B3.14%2F4%29%281%29%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%92%8C%E5%9B%BE%E5%83%8F%E7%9A%84%E5%AF%B9%E7%A7%B0%E8%BD%B4%E6%96%B9%E7%A8%8B+%EF%BC%882%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5B-3.14%2F12%2C3.14%2F2%5D%E4%B8%8A%E7%9A%84%E5%80%BC%E5%9F%9F)
已知函数f(x)=cos(2x-3.14/3)+2sin(x-3.14/4)sin(x+3.14/4)(1)求函数f(x)的最小正周期和图像的对称轴方程 (2)求函数f(x)在区间[-3.14/12,3.14/2]上的值域
已知函数f(x)=cos(2x-3.14/3)+2sin(x-3.14/4)sin(x+3.14/4)
(1)求函数f(x)的最小正周期和图像的对称轴方程
(2)求函数f(x)在区间[-3.14/12,3.14/2]上的值域
已知函数f(x)=cos(2x-3.14/3)+2sin(x-3.14/4)sin(x+3.14/4)(1)求函数f(x)的最小正周期和图像的对称轴方程 (2)求函数f(x)在区间[-3.14/12,3.14/2]上的值域
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
(1)求函数f(x)的最小正周期和图像的对称轴方程
(2)求函数f(x)在区间[-π/12,π/2]上的值域
⑴f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
=cos(2x-π/3)+√2sinx(x-π/4)√2sin(x+π/4)
=cos(2x-π/3)+(sinx-cosx)(sinx+cosx)
=cos(2x-π/3)+(sinx^2-cosx^2)
=cos(2x-π/3)+cos2x
=1/2cos2x-√3/2sin2x+cos2x
=3/2cos2x-√3/2sin2x
=√3(√3/2cos2x-1/2sin2x)
=√3sin(2x-π/3)
∴函数f(x)的最小正周期为π,图像的对称轴方程 x=kπ/2+π/6
(2)函数f(x)在区间[-π/12,π/2]上的值域 [-√3,√3]