设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).求m,n的值.(2)若f(x)=2+根号3,求x的值
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![设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).求m,n的值.(2)若f(x)=2+根号3,求x的值](/uploads/image/z/8832773-29-3.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dmcos%26%23178%3Bx%2B%E2%88%9A3msinxcosx%2Bn%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%E3%80%900%2C30%C2%B0%E3%80%91.%E5%80%BC%E5%9F%9F%E4%B8%BA%E3%80%903%2C4%E3%80%91%EF%BC%881%EF%BC%89.%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dmcos%26%23178%3Bx%2B%E2%88%9A3msinxcosx%2Bn%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%E3%80%900%2C30%C2%B0%E3%80%91.%E5%80%BC%E5%9F%9F%E4%B8%BA%E3%80%903%2C4%E3%80%91%EF%BC%881%EF%BC%89.%E6%B1%82m%2Cn%E7%9A%84%E5%80%BC.%EF%BC%882%EF%BC%89%E8%8B%A5f%28x%29%3D2%2B%E6%A0%B9%E5%8F%B73%2C%E6%B1%82x%E7%9A%84%E5%80%BC)
设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).求m,n的值.(2)若f(x)=2+根号3,求x的值
设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).
设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).求m,n的值.(2)若f(x)=2+根号3,求x的值
设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).设函数f(x)=mcos²x+√3msinxcosx+n的定义域为【0,30°】.值域为【3,4】(1).求m,n的值.(2)若f(x)=2+根号3,求x的值
f(x)=mcos²x+√3msinxcosx+n
=m/2(1+cos2x)+√3/2msin2x+n
=m(√3/2sin2x+1/2cos2x)+m/2+n
=msin(2x+π/6)+m/2+n
∵x∈【0,π/6】.
∴2x+π/6∈[π/6,π/2]
∴1/2≤sin(2x+π/6)≤1
f(x)的值域为[3,4]
当m>0时,
f(x)max=3/2m+n=4
f(x)min=m+n=3
解得m=2,n=1
当m<0时,
f(x)min=3/2m+n=3
f(x)max=m+n=4
解得m=-2,n=6
(2)
m=2时,
f(x)=2sin(2x+π/6)+2
f(x)=2+√3,
sin(2x+π/6)=√3/2
∴2x+π/6=π/3,
x=π/12
当m=-2时,
f(x)=-2sin(2x+π/6)+5
f(x)=2+√3,
sin(2x+π/6)=(3-√3)/2
∴2x+π/6=arcsin(3-√3)/2
∴x=1/2arcsin(3-√3)/2-π/12