如题 第二小问的最小值怎么求
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(2) f(x)=sin(2x-π/3)
f(x)横坐标缩短到原来的1/2倍,周期T=π/2,ω=2π/(π/2)=4,得到sin(4x-π/3)。
向左平移π/6个单位长度,得到g(x)=sin[4(x+π/6)-π/3]
=sin(4x+2π/3-π/3)
=sin(4x+π/3)
即:g(x)=sin(4x+π/3)
x∈[0,π/8]
4x∈[0,π/2]
4x+π/3∈[π/3,5π/6]
sin(4x+π/3)∈[1/2,1]
当4x+π/3=5π/6时,g(x)取得最小值:g(x)min=sin(5π/6)=1/2
f(x)横坐标缩短到原来的1/2倍,周期T=π/2,ω=2π/(π/2)=4,得到sin(4x-π/3)。
向左平移π/6个单位长度,得到g(x)=sin[4(x+π/6)-π/3]
=sin(4x+2π/3-π/3)
=sin(4x+π/3)
即:g(x)=sin(4x+π/3)
x∈[0,π/8]
4x∈[0,π/2]
4x+π/3∈[π/3,5π/6]
sin(4x+π/3)∈[1/2,1]
当4x+π/3=5π/6时,g(x)取得最小值:g(x)min=sin(5π/6)=1/2
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