已知函数f(x)=cosx^2-sinx^2+(2根号3)sinxcosx+11.求f(x)的最小正周期及最小值2.若f(a)=2,且a属于【π/4,π/2】,求a的值
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![已知函数f(x)=cosx^2-sinx^2+(2根号3)sinxcosx+11.求f(x)的最小正周期及最小值2.若f(a)=2,且a属于【π/4,π/2】,求a的值](/uploads/image/z/2625791-23-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dcosx%5E2-sinx%5E2%2B%282%E6%A0%B9%E5%8F%B73%29sinxcosx%2B11.%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%8F%8A%E6%9C%80%E5%B0%8F%E5%80%BC2.%E8%8B%A5f%EF%BC%88a%EF%BC%89%3D2%2C%E4%B8%94a%E5%B1%9E%E4%BA%8E%E3%80%90%CF%80%2F4%2C%CF%80%2F2%E3%80%91%2C%E6%B1%82a%E7%9A%84%E5%80%BC)
已知函数f(x)=cosx^2-sinx^2+(2根号3)sinxcosx+11.求f(x)的最小正周期及最小值2.若f(a)=2,且a属于【π/4,π/2】,求a的值
已知函数f(x)=cosx^2-sinx^2+(2根号3)sinxcosx+1
1.求f(x)的最小正周期及最小值
2.若f(a)=2,且a属于【π/4,π/2】,求a的值
已知函数f(x)=cosx^2-sinx^2+(2根号3)sinxcosx+11.求f(x)的最小正周期及最小值2.若f(a)=2,且a属于【π/4,π/2】,求a的值
f(x)=cosx^2-sinx^2+(2根号3)sinxcosx+1
= cos2x + 根号3sin2x + 1
= 2( 根号3/2 sin2x+ 1/2 cos2x ) + 1
= 2( sin2xcosπ/6 + cos2xsinπ/6 ) + 1
= 2 sin(2x+π/6) + 1
最小正周期 = 2π/2 = π
最小值 = 2*(-1)+1 = -1
f(a)=2
2 sin(2a+π/6) + 1 = 2
sin(2a+π/6) = 1/2
a属于【π/4,π/2】
2a∈【π/2,π】
2a+π/6∈【2π/3,7π/6】
2a+π/6 = 5π/6
a = π/3
f(x)=cosx^2-sinx^2+(2根号3)sinxcosx+1=cos2x+根号3倍sin2x+1
=2(1/2cos2x+二分之根号3倍sin2x)
=2(sin30度*cos23+cos30度*sin2x)+1
=2sin(zx+30度)+1
最小正周期为pai
2sin(2a+30度)+1=2,
sin(2a+30度)=1/2
因为a属于【π/4,π/2】所以a=π/3