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已知向量a=(sinx/3,cosx/3),向量b=(cosx/3,根号3 cosx/30 ,函数f(x)=向量a*b
(1)将f(x)写成Asin(wx+)的形式,并求其图象对称中心的坐标;
(2)如果△ABC 的三边a,b,c 满足b^2=ac ,且边b 所对的角为x ,试求x 的范围及此时函数f(x) 的值域.
人气:247 ℃ 时间:2019-08-20 17:19:01
解答
1) f(x)=a*b=sin(x/3)*cos(x/3)+cos(x/3)*√3cos(x/3)=2cos(x/3)[1/2sin(x/3)+√3/2cos(x/3)]=2cos(x/3)sin(x/3+π/3)=sin(x/3+x/3+π/3)-sin(x/3-x/3-π/3)=sin(2x/3+π/3)+sin(π/3)=sin(2x/3+π/3)+√3/2图像对称...=2cos(x/3)sin(x/3+π/3) =sin(x/3+x/3+π/3)-sin(x/3-x/3-π/3)怎么算三角公式的积化和差公式:2cosαsinβ=sin(α+β)-sin(α-β)
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