f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π),将f(x)的图像向右平移π/6个单位求在[0,π]上的最大值和最少值
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![f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π),将f(x)的图像向右平移π/6个单位求在[0,π]上的最大值和最少值](/uploads/image/z/11512987-43-7.jpg?t=f%28x%29%3D2%E6%A0%B9%E5%8F%B73sin%28x%2F2%2B%CF%80%2F4%29cos%28x%2F2%2B%CF%80%2F4%29-sin%28x%2B%CF%80%29%2C%E5%B0%86f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%9B%BE%E5%83%8F%E5%90%91%E5%8F%B3%E5%B9%B3%E7%A7%BB%CF%80%2F6%E4%B8%AA%E5%8D%95%E4%BD%8D%E6%B1%82%E5%9C%A8%5B0%2C%CF%80%5D%E4%B8%8A%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E5%92%8C%E6%9C%80%E5%B0%91%E5%80%BC)
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f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π),将f(x)的图像向右平移π/6个单位求在[0,π]上的最大值和最少值
f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π),将f(x)的图像向右平移π/6个单位求在[0,π]上
的最大值和最少值
f(x)=2根号3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π),将f(x)的图像向右平移π/6个单位求在[0,π]上的最大值和最少值
f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3*23sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3sin(x+π/2)-sin(x+π)
=√3cosx+sinx
=2cos(x-π/6)
将f(x)的图像向右平移π/6个单位
则g(x)=f(x-π/6)=2cos(x-π/3)
∴在[0,π]上,当x=π/3时有最大值2,当x=π时有最小值-1
f(X)=√3 sin(x+π/2)+sin x
=√3 cos x +sin x
=2[√3/2* cos x +1/2*sin x]
=2[ sin π/3* cosx + cos π/3* sinx]
=2sin(x+π/3)
将f(x)的图像向右平移π/6个单位,画出图形得知,在[0,π]上,π/6处取最大值为2,π处最小值为-1。
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