作业帮y=sin(x-π/6)sin(x+π/3)最小正周期
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 17:10:28
y=sin(x-π/6)sin(x+π/3)最小正周期
y=sin(x-π/6)sin(x+π/3)最小正周期
y=sin(x-π/6)sin(x+π/3)最小正周期
y=sin(x-π/6)sin(x+π/3)
=-cos(x-π/6+π/2)sin(x+π/3)
=-cos(x+π/3)sin(x+π/3)
=-sin(2x+2π/3)/2
T=2π/2=π
y=sin(x-π/6)sin(x+π/3)
=sin(x-π/6)*cos[π/2-(x-π/3)]
=sin(x-π/6)cos(π/6-x)
=sin(x-π/6)cos(x-π/6)
=1/2sin(2x-π/3)
所以，最小正周期T=2 π/2=π
判断单调性 y=sin(x-π/6) y=sin(-2x+π/3)
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