函数y=cos^2ωx-sin^2ωx(ω>0)的最小正周期是π,则函数f(x)=2sin(ωx+π/4)的一个单调增区间是?A.[-π/2,π/2] B[5π/4,9π/4] C.[-π/4,3π/4] D.[π/4,5π/4]
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![函数y=cos^2ωx-sin^2ωx(ω>0)的最小正周期是π,则函数f(x)=2sin(ωx+π/4)的一个单调增区间是?A.[-π/2,π/2] B[5π/4,9π/4] C.[-π/4,3π/4] D.[π/4,5π/4]](/uploads/image/z/3016819-19-9.jpg?t=%E5%87%BD%E6%95%B0y%3Dcos%5E2%CF%89x-sin%5E2%CF%89x%28%CF%89%3E0%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E6%98%AF%CF%80%2C%E5%88%99%E5%87%BD%E6%95%B0f%28x%29%3D2sin%28%CF%89x%2B%CF%80%2F4%29%E7%9A%84%E4%B8%80%E4%B8%AA%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4%E6%98%AF%3FA.%5B-%CF%80%2F2%2C%CF%80%2F2%5D+B%5B5%CF%80%2F4%2C9%CF%80%2F4%5D+C.%5B-%CF%80%2F4%2C3%CF%80%2F4%5D+D.%5B%CF%80%2F4%2C5%CF%80%2F4%5D)
函数y=cos^2ωx-sin^2ωx(ω>0)的最小正周期是π,则函数f(x)=2sin(ωx+π/4)的一个单调增区间是?A.[-π/2,π/2] B[5π/4,9π/4] C.[-π/4,3π/4] D.[π/4,5π/4]
函数y=cos^2ωx-sin^2ωx(ω>0)的最小正周期是π,则函数f(x)=2sin(ωx+π/4)的一个单调增区间是?
A.[-π/2,π/2] B[5π/4,9π/4] C.[-π/4,3π/4] D.[π/4,5π/4]
函数y=cos^2ωx-sin^2ωx(ω>0)的最小正周期是π,则函数f(x)=2sin(ωx+π/4)的一个单调增区间是?A.[-π/2,π/2] B[5π/4,9π/4] C.[-π/4,3π/4] D.[π/4,5π/4]
y=cos^2ωx-sin^2ωx=cos(2ωx)最小正周期为π,所以2ω=正负2,即ω=正负1,又ω>0,故ω=1.
所以,f(x)=2sin(ωx+π/4)=2sin(x+π/4).
单增区间为[-3π/4,π/4] ,[5π/4,9π/4]
答案是B
y=cos^2ωx-sin^2ωx=cos(2ωx)最小正周期为π,所以2ω=正负2,即ω=正负1,又ω>0,故ω=1.
所以,f(x)=2sin(ωx+π/4)=2sin(x+π/4)。
单增区间为[-3π/4,π/4] ,[5π/4,9π/4]
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