设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期1.求f(π/2)的值2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值

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设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期1.求f(π/2)的值2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值
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设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期1.求f(π/2)的值2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值
设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期
1.求f(π/2)的值
2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值

设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期1.求f(π/2)的值2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值
函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期
则T=2π/w=π
w=2
所以 f(x)=2sin(2x+π/3)
(1) f(π/2)=2sin(π+π/3)=-2sin(π/3)=-√3
(2)f(a/2+π/12)=2sin(a+π/6+π/3)=2cosa=10/13
cosa=5/13
a∈(-π/2,0)
sina=-12/13
sin(a-π/4)=sinacos(π/4)-cosasin(π/4)=-12/13*(√2/2)-(5/13)*(√2/2)=-17√2/26

(1) f(x)=2sin(wx-π/6)•sin(wx+π/2-π/6)
=2sin[π/2+(wx-π/6)]•sin(wx-π/6)
=2cos(wx-π/6)•sin(wx-π/6)
=sin(2wx-π/3)
因周期T=2π/2w=π,则w=1
所以f(x)=sin(2x-π/3)
在三角形ABC中,若A...

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(1) f(x)=2sin(wx-π/6)•sin(wx+π/2-π/6)
=2sin[π/2+(wx-π/6)]•sin(wx-π/6)
=2cos(wx-π/6)•sin(wx-π/6)
=sin(2wx-π/3)
因周期T=2π/2w=π,则w=1
所以f(x)=sin(2x-π/3)
在三角形ABC中,若A〈B,且f(A)=f(B)=1/2
则由f(x)=sin(2x-π/3)=1/2,
知2A-π/3=π/6,A=π/4
2x-π/3=π-π/6,B=7π/12
所以C=π-A-B=π-π/4-7π/12=π/6
由正弦定理BC/AB=sinA/sinC
=sin(π/4)/sin(π/6)
=(√2/2)/(1/2)
=√2
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