求y=2sin(2x+π/3)-1的值域,x属于(π/6,2π/3)

显示全部楼层 · 2012-12-4 12:22:52

π/6<x<2π/32π/3<2x+π/3<2π所以sin(3π/2)-<sin(2x+π/3)<sin2π/3所以-2<=y<√3/2-1值域[-2，√3/2-1)...

千问 · 2012-12-4 12:22:52

解：令y=2x-π/3，则：f(y)=2siny此时：x=y/2-π/6，当x∈[π/6,2π/3]，有：y∈[0,π]对于f(y)=2siny，当y∈[0,π]时，有：f(y)∈[0,1]所以，对于f(x)=sin(2x-π/3)，当x∈[π/6,2π/3]时，有：f(x)∈[0,1]即所求值域是：0≤f(x)≤1。...