求函數(shù)y=2sin(2x-π/6)的值域,單調(diào)區(qū)間,對稱軸,對稱點,

數(shù)學人氣：351 ℃時間：2019-11-18 19:36:38

優(yōu)質(zhì)解答

1.當2x-π/6=π/2+2kπ,即當x=π/3+kπ,(k∈Z)時,ymax=2×1=2,
當2x-π/6=3π/2+2kπ,即x=5π/6+kπ,(k∈Z)時,ymin=2×(-1)=-2,∴值域[-2,2].
2.由-π/2+2kπ≤2x-π/6≤π/2+2kπ,得-π/6+kπ≤x≤π/3+kπ,k∈Z,
單增區(qū)間是[-π/6+kπ,π/3+kπ],k∈Z；
由π/2+2kπ≤2x-π/6≤3π/2+2kπ,得π/3+kπ≤x≤5π/6+kπ,k∈Z,
單減區(qū)間是[π/3+kπ,5π/6+kπ],k∈Z.,
3.由2x-π/6=π/2+kπ,k∈Z,得對稱軸為x=π/3+(1/2)kπ,k∈Z.
4.由2x-π/6=kπ,得x=π/12+(1/2)kπ,k∈Z,∴對稱中心是(π/12+kπ/2,0),k∈Z.