设函数f(x)=cosx+√3sinX,

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设函数f(x)=cosx+√3sinX,

设函数f(x)=cosx+√3sinX,
设函数f(x)=cosx+√3sinX,

设函数f(x)=cosx+√3sinX,
(1)原函数提出2后,等于f(x)=2sin(x+π/6),所以值域是正负1/2,周期是2π
(2)可得点A坐标(π/6,√3),根据正弦定理得sinA/a=sinB/b,所以sinA/sinB=a/b=√2/2 所以角A是30°,角B是60°,角C是90°

(1)求函数f(x)的值域和周期
f(x)=cosx+√3sinX
=2(0.5cosx+√3/2sinx)
=2(sinπ/6cosx+cosπ/6sinx)
=2sin(x+π/6)
-1≤sin(x+π/6)≤2
函数f(x)的值域是[-2,2]
函数f(x)的周期是2π
(2)在△ABC中,f(A)=√3,有
sin(...

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(1)求函数f(x)的值域和周期
f(x)=cosx+√3sinX
=2(0.5cosx+√3/2sinx)
=2(sinπ/6cosx+cosπ/6sinx)
=2sin(x+π/6)
-1≤sin(x+π/6)≤2
函数f(x)的值域是[-2,2]
函数f(x)的周期是2π
(2)在△ABC中,f(A)=√3,有
sin(A+π/6)=√3/2
所以A+π/6=π/3,A+π/6=2π/3
得A=π/6或A=π/2
由a=b√2/2得
A=π/6
sinB=√2/2
B=π/4或B=3π/4
所以C=7π/12或C=π/12

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