已知函数f(x)=sin[x+(π/3)]sin[x+(π/2)].(1)求f(x)的最小正周期.(2)若g(x)=f(x)-[(根号3)/4]..求g(x)在区间[0,π/2]上的值域.
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![已知函数f(x)=sin[x+(π/3)]sin[x+(π/2)].(1)求f(x)的最小正周期.(2)若g(x)=f(x)-[(根号3)/4]..求g(x)在区间[0,π/2]上的值域.](/uploads/image/z/13300152-24-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%5Bx%2B%28%CF%80%2F3%29%5Dsin%5Bx%2B%28%CF%80%2F2%29%5D.%281%29%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F.%EF%BC%882%EF%BC%89%E8%8B%A5g%EF%BC%88x%EF%BC%89%3Df%EF%BC%88x%EF%BC%89-%5B%EF%BC%88%E6%A0%B9%E5%8F%B73%29%2F4%5D..%E6%B1%82g%EF%BC%88x%EF%BC%89%E5%9C%A8%E5%8C%BA%E9%97%B4%5B0%2C%CF%80%2F2%5D%E4%B8%8A%E7%9A%84%E5%80%BC%E5%9F%9F.)
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已知函数f(x)=sin[x+(π/3)]sin[x+(π/2)].(1)求f(x)的最小正周期.(2)若g(x)=f(x)-[(根号3)/4]..求g(x)在区间[0,π/2]上的值域.
已知函数f(x)=sin[x+(π/3)]sin[x+(π/2)].(1)求f(x)的最小正周期.
(2)若g(x)=f(x)-[(根号3)/4]..求g(x)在区间[0,π/2]上的值域.
已知函数f(x)=sin[x+(π/3)]sin[x+(π/2)].(1)求f(x)的最小正周期.(2)若g(x)=f(x)-[(根号3)/4]..求g(x)在区间[0,π/2]上的值域.
f(x)=sin(x+π/3)*cosx
=sinxcos(π/3)cosx+cosxsin(π/3)*cosx
=(1/4)sin2x+(√3/4)(1+cos2x)
=(1/4)sin2x+(√3/4)cos2x+√3/4
=(1/2)sin(2x+π/3)+√3/4
(1)周期是T=2π/2=π
(2) g(x)=(1/2)sin(2x+π/3)
x∈[0,π/2]
∴ 2x+π/3∈[π/3,4π/3)
∴ 2x+π/3=π/2时,y有最大值1/2
2x+π/3=4π/3时,y有最小值-√3/4
即值域是[-√3/4,1/2]
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