f(x)=根号3sin2x-2sin平方x (1).求f(x)最大值 (2).求f(x)的零点的集合
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f(x)=根号3sin2x-2sin平方x (1).求f(x)最大值 (2).求f(x)的零点的集合
f(x)=根号3sin2x-2sin平方x (1).求f(x)最大值 (2).求f(x)的零点的集合
f(x)=根号3sin2x-2sin平方x (1).求f(x)最大值 (2).求f(x)的零点的集合
f(x)=(√3)sin2x-2sin²x ;(1).求f(x)最大值 (2).求f(x)的零点的集合
(1)f(x)=(√3)sin2x+cos2x-1=2[(√3/2)sin2x+(1/2)cos2x]-1=2[sin2xcos(π/6)+cos2xsin(π/6)]-1
=2sin(2x+π/6)-1
-2≦2sin(2X+π/6)≦2,-3≦2sin(2x+π/6)-1≦1
即-3≦f(x)≦1,故f(x)的最大值是1,最小值是-3.
(2)令f(x)=2sin(2x+π/6)-1=0
得sin(2x+π/6)=1/2,故2x+π/6=π/6+2kπ,x=kπ,k∈Z.
(1)f(x)=√3sin2x-2sin²x
=2√3sinxcosx-2sin²x
=4sinx(√3/2cosx-1/2sinx)
=4sinxsin(60°-x)
=4×(-1/2)[cos(x+60°-x)-cosx(x-60°+x)]
=2cos(2x-60°)-1
∵co...
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(1)f(x)=√3sin2x-2sin²x
=2√3sinxcosx-2sin²x
=4sinx(√3/2cosx-1/2sinx)
=4sinxsin(60°-x)
=4×(-1/2)[cos(x+60°-x)-cosx(x-60°+x)]
=2cos(2x-60°)-1
∵cos(2x-60°)∈[-1,1]
∴f(x)=2cos(2x-60°)-1∈[-3,1]
∴f(x)max=1
(2) f(x)=0,则
2cos(2x-60°)-1=0
cos(2x-60°)=1/2=cos(2kП+60°) K∈Z
2x-60°=2kП+60°
x=kП+60°
收起
1)
f(x)=(√3)sin2x+cos2x-1
=2sin(2x+π/6)-1
f(x)最大值为1
2)
当2x+π/6= π/6或5π/6 时f(x)为0
解得x=kπ和x=π/3+kπ K∈Z