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已知函数f(x)=sin(wx+φ)(w>0,0≦φ≦π)为偶函数,且其图象上相临的两对称轴之间的距离为2兀.1)求f(

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已知函数f(x)=sin(wx+φ)(w>0,0≦φ≦π)为偶函数,且其图象上相临的两对称轴之间的距离为2兀.1)求f(x)的解
已知函数f(x)=sin(wx+φ)(w>0,0≦φ≦π)为偶函数,且其图象上相临的两对称轴之间的距离为2兀(.1)求f(x)的解析式(2)若a属于(-π/3,π/2),且f(a+π/3)=1/3,求sin(2a+5π/3)
已知函数f(x)=sin(wx+φ)(w>0,0≦φ≦π)为偶函数,且其图象上相临的两对称轴之间的距离为2兀.1)求f(
已知函数f(x)=sin(wx+φ)(w>0,0≦φ≦π)为偶函数,且其图象上相临的两对称轴之间的距离为2兀(.1)求f(x)的解析式(2)若a属于(-π/3,π/2),且f(a+π/3)=1/3,求sin(2a+5π/3)
(1)解析:∵函数f(x)=sin(wx+φ)(w>0,0≦φ≦π)为偶函数,且其图象上相临的两对称轴之间的距离为2兀
∴T/2=2π==>T=4π==>w=1/2
∴f(x)=sin(1/2x+φ)=sin(1/2(x+2φ))==>2φ=-π==>φ=-π/2
或f(x)=sin(1/2x+φ)=sin(1/2(x+2φ))==>2φ=π==>φ=π/2
∴f(x)=sin(1/2x+π/2)或f(x)=sin(1/2x-π/2)
(2)解析:∵a属于(-π/3,π/2),且f(a+π/3)=1/3
f(x)=sin(1/2x+π/2)==> f(a+π/3)=sin(1/2a+π/6+π/2)=1/3
设θ=1/2a+π/6+π/2==>a=2θ-4π/3
sin(2a+5π/3)= sin(2(2θ-4π/3)+5π/3)=sin(4θ-π)=-sin4θ
-π/3