已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)(1)求f(x)的最小正周期(2)若将f(x)的图像向右平移π/6个单位,得到函数g(x)的图像,求函数g(x)在区间[0,π]的最大值和最小值
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已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)(1)求f(x)的最小正周期(2)若将f(x)的图像向右平移π/6个单位,得到函数g(x)的图像,求函数g(x)在区间[0,π]的最大值和最小值
已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)(1)求f(x)的最小正周期(2)若将f(x)的图像向右平移π/6个单位,得到函数g(x)的图像,求函数g(x)在区间[0,π]的最大值和最小值
已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)(1)求f(x)的最小正周期(2)若将f(x)的图像向右平移π/6个单位,得到函数g(x)的图像,求函数g(x)在区间[0,π]的最大值和最小值
f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3sin(x+π/2)+sinx
=√3cosx+sinx
=2(√3/2cosx+1/2*sinx)
=2sin(x+π/3)
∴f(x)的最小正周期T=2π
(2)将f(x)的图像向右平移π/6个单位,得到函数
g(x)=2sin(x-π/6+π/3)=2sin(x+π/6)
∵x∈[0,π],∴x+π/6∈[π/6,7π/6]
∴x+π/6=π/2时,g(x)取得最大值2
x=7π/6时,g(x)取得最小值-1
f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3sin(x+π/2)+sinx
=√3cosx+sinx
=2(√3/2cosx+1/2*sinx)
=2sin(x+π/3)
∴f(x)的最小正周期T=2π
(2)将f(x)的图像向右平移π/6个单位,得到函数
g(x...
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f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3sin(x+π/2)+sinx
=√3cosx+sinx
=2(√3/2cosx+1/2*sinx)
=2sin(x+π/3)
∴f(x)的最小正周期T=2π
(2)将f(x)的图像向右平移π/6个单位,得到函数
g(x)=2sin(x-π/6+π/3)=2sin(x+π/6)
∵x∈[0,π],∴x+π/6∈[π/6,7π/6]
∴x+π/6=π/2时，g(x)取得最大值2
x=7π/6时，g(x)取得最小值-1
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f(x)=2√3sin(x/2 π/4)cos(x/2 π/4)-sin(x π)
=√3sin(x π/2) sinx
=√3cosx sinx
=2(√3/2cosx 1/2*sinx)
=2sin(x π/3)
∴f(x)的最小正周期T=2π
(2)将f(x)的图像向右平移π/6个单位,得到函数
g(x)=2sin(x-π/6 π/3)...
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f(x)=2√3sin(x/2 π/4)cos(x/2 π/4)-sin(x π)
=√3sin(x π/2) sinx
=√3cosx sinx
=2(√3/2cosx 1/2*sinx)
=2sin(x π/3)
∴f(x)的最小正周期T=2π
(2)将f(x)的图像向右平移π/6个单位,得到函数
g(x)=2sin(x-π/6 π/3)=2sin(x π/6)
∵x∈[0,π],∴x π/6∈[π/6,7π/6]
∴x π/6=π/2时，g(x)取得最大值2
x=7π/6时，g(x)取得最小值-1
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