已知偶函数f(x)=sin(ωx+φ)+cos(ωx+φ)(ω>0,|φ|<π/2)的最小正周期为π,则f(x)的初相为?
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![已知偶函数f(x)=sin(ωx+φ)+cos(ωx+φ)(ω>0,|φ|<π/2)的最小正周期为π,则f(x)的初相为?](/uploads/image/z/3742138-10-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%81%B6%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28%CF%89x%2B%CF%86%29%2Bcos%28%CF%89x%2B%CF%86%29%28%CF%89%EF%BC%9E0%2C%7C%CF%86%7C%EF%BC%9C%CF%80%2F2%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E4%B8%BA%CF%80%2C%E5%88%99f%28x%29%E7%9A%84%E5%88%9D%E7%9B%B8%E4%B8%BA%3F)
已知偶函数f(x)=sin(ωx+φ)+cos(ωx+φ)(ω>0,|φ|<π/2)的最小正周期为π,则f(x)的初相为?
已知偶函数f(x)=sin(ωx+φ)+cos(ωx+φ)(ω>0,|φ|<π/2)的最小正周期为π,则f(x)的初相为?
已知偶函数f(x)=sin(ωx+φ)+cos(ωx+φ)(ω>0,|φ|<π/2)的最小正周期为π,则f(x)的初相为?
合并为根2倍*sin(ωx+φ+π/4)
T=π→ω=2;
又∵根2倍*sin(2x+φ+π/4)为偶函数
结合条件,φ+π/4=π/2
∴φ=π/4