已知函數(shù)f(x)=Asin(ωx-π/3),(A>0,ω>0的圖像經(jīng)過(π,2),且其單調(diào)遞增區(qū)間最大長度為2π,求函數(shù)解析式

數(shù)學(xué)人氣：187 ℃時間：2019-11-21 04:18:53

優(yōu)質(zhì)解答

函數(shù)f(x)=Asin(ωx-π/3),(A>0,ω>0的圖像經(jīng)過(π,2),其單調(diào)遞增區(qū)間最大長度為2π,
T=4π
2π/ω=4π
ω=1/2
Asin(π/2-π/3)=2
A=4
函數(shù)解析式:f(x)=4sin(x/2-π/3)若g(x)=f(x+3π），求g(x)的單調(diào)區(qū)間。g(x)=f(x+3π）=4sin[(x+3π)/2-π/3]=4sin(x/2+7π/6)由2kπ-π/2<=x/2+7π/6<=2kπ+π/2解得，g(x)的單調(diào)增區(qū)間：[ ,]由2kπ+π/2<=x/2+7π/6<=2kπ+3π/2解得，g(x)的單調(diào)減區(qū)間：[ ,]，自己解吧