这道题怎么写?
3个回答
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由题意f(x)的最大值=f(π/6),最小值=f(-5π/6),
则π/6-(-5π/6)=kT/2,
T=2π/k,k∈N*
又T=2π/ω,得ω=2k/3
最小正周期最大,ω最小,即ω=2/3,
f(π/6)=√3sin(π/6+φ)=√3,
│φ│<π/2,则φ=π/3,
f(x)=√3sin(x+π/3),
单调递增区间满足2kπ-π/2≤x+π/3≤2kπ+π/2,
得2kπ-5π/6≤x≤2kπ+π/6,
由上f(a+π/6)=√3sin(a+π/2)=√3cosa=3√3/5
cosa=3/5,则sina=4/5
得sin2a=24/25,cos2a=-7/25
f(2a)=√3sin(2a+π/3)=√3/2*sin2a+3/2*cos2a=12√3/25-21/50
则π/6-(-5π/6)=kT/2,
T=2π/k,k∈N*
又T=2π/ω,得ω=2k/3
最小正周期最大,ω最小,即ω=2/3,
f(π/6)=√3sin(π/6+φ)=√3,
│φ│<π/2,则φ=π/3,
f(x)=√3sin(x+π/3),
单调递增区间满足2kπ-π/2≤x+π/3≤2kπ+π/2,
得2kπ-5π/6≤x≤2kπ+π/6,
由上f(a+π/6)=√3sin(a+π/2)=√3cosa=3√3/5
cosa=3/5,则sina=4/5
得sin2a=24/25,cos2a=-7/25
f(2a)=√3sin(2a+π/3)=√3/2*sin2a+3/2*cos2a=12√3/25-21/50
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