【高中数学题】【在线等】【必采纳】已知函数f(x)=cos(2x-5π/3)+2sin(x-π/4)sin(x+π/4)

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/11 00:31:45

【高中数学题】【在线等】【必采纳】已知函数f(x)=cos(2x-5π/3)+2sin(x-π/4)sin(x+π/4)
（1）求函数的最小正周期和对称轴方程
（2）求函数f（x）在区间[-π/12,π/2]值域

f(x)=cos(2x-5π/3)+2sin(x-π/4)sin(x+π/4)
=cos(2x-2π/3-π)+cosπ/2-cos2x 积化和差公式：sinαsinβ=[-cos(α+β)+cos(α-β)]/2
=-cos(2x-2π/3)-cos2x
=sin2xsin2π/3-cos2xcos2π/3-cos2x
=(√3/2)sin2x-(-1/2)cos2x-cos2x
=(√3/2)sin2x-(1/2)cos2x
=sin(2x-π/6)
最小正周期 T=2π/2=π
对称轴为 2x-π/6=2kπ
x=π/12+kπ k=0,1,2.
(2)自己画图即可看出
很高兴为您解答,祝你学习进步!【胖教育】团队为您答题.
有不明白的可以追问!如果您认可我的回答.
请点击下面的【选为满意回答】按钮,谢谢!

【高中数学题】【在线等】【必采纳】已知函数f(x)=cos(2x-5π/3)+2sin(x-π/4)sin(x+π/4) 已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) 已知函数f(x)=sin^2*x-根号3*sinπ/4*x*cosπ/4*x 已知函数f(x)=cos(2x-π/3)+sin^2 x-cos^2 x 已知函数f(x)=cos(2x-π\3)+sin²x-cos²x 已知函数f(x)=cos(2x-π/3）+2sin(x-π/4）sin(x+π/4)=sin(2x-π/6) , 已知函数f(x0=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) 已知函数f(x)=2sin(x/4)cos(x/4)-2√3sin²（x/4)+√3,且g(x)=f(x+π/ 已知函数f(x)=(1+1/tanx)sin(x)^2 -2sin(x+π/4)*cos(x+π/4) 已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) 求函数f(x 已知函数f(x)=2sin(x+π/4)cos(x-π/4) 已知函数f(x)= [sin(2π-x)sin(π+x)cos(-x-π)] ／[2cos(π-x)sin(3π-x)]