设函数f(x)=cos(2x-π/3)+2sin^2(x+π/2) 求f(x)的最小正周期和对称轴方程当x∈【-π/3,π/4】时,求f(x)的值域
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![设函数f(x)=cos(2x-π/3)+2sin^2(x+π/2) 求f(x)的最小正周期和对称轴方程当x∈【-π/3,π/4】时,求f(x)的值域](/uploads/image/z/1858894-70-4.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dcos%282x-%CF%80%2F3%29%2B2sin%5E2%28x%2B%CF%80%2F2%EF%BC%89+%E6%B1%82f%EF%BC%88x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%92%8C%E5%AF%B9%E7%A7%B0%E8%BD%B4%E6%96%B9%E7%A8%8B%E5%BD%93x%E2%88%88%E3%80%90-%CF%80%2F3%2C%CF%80%2F4%E3%80%91%E6%97%B6%2C%E6%B1%82f%28x%29%E7%9A%84%E5%80%BC%E5%9F%9F)
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设函数f(x)=cos(2x-π/3)+2sin^2(x+π/2) 求f(x)的最小正周期和对称轴方程当x∈【-π/3,π/4】时,求f(x)的值域
设函数f(x)=cos(2x-π/3)+2sin^2(x+π/2) 求f(x)的最小正周期和对称轴方程
当x∈【-π/3,π/4】时,求f(x)的值域
设函数f(x)=cos(2x-π/3)+2sin^2(x+π/2) 求f(x)的最小正周期和对称轴方程当x∈【-π/3,π/4】时,求f(x)的值域
这是高一的题目吧,复习加油,
1、f(x)=cos2xcosπ/3+sin2xsinπ/3+1-cos(2x+π)
=cos2x*1/2+sin2x*√3/2+1+cos2x
=cos2x*3/2+sin2x*√3/2+1
=√3(cos2x*√3/2+sin2x*1/2)+1
=√3(cos2xcosπ/6+sin2xsinπ/6)+1
=√3cos(2x-π/6)+1
所以T...
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1、f(x)=cos2xcosπ/3+sin2xsinπ/3+1-cos(2x+π)
=cos2x*1/2+sin2x*√3/2+1+cos2x
=cos2x*3/2+sin2x*√3/2+1
=√3(cos2x*√3/2+sin2x*1/2)+1
=√3(cos2xcosπ/6+sin2xsinπ/6)+1
=√3cos(2x-π/6)+1
所以T=π
对称轴则cos(2x-π/6)=±1
2x-π/6=kπ
x=kπ/2+π/12
2、
-π/3<=x<=π/4
-5π/6<=2x-π/6<=π/3
所以最大是cos0=1
最小是cos(-5π/6)=-√3/2
所以值域是[-1/2,√3+1]
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