设函数f(x)=√3cos²x+sinxcosx-√3\/2(1)求函数f(x)的最小正周期T...
f(x)=√3cos²x+sinxcosx-√3\/2 =(√3\/2)[cos(2x)+1]+(1\/2)sin(2x)-√3\/2 =(√3\/2)cos(2x)+(1\/2)sin(2x)=cos(π\/6)cos(2x)+sin(π\/6)sin(2x)=cos(2x-π\/6)最小正周期T=2π\/2=π 2kπ-π≤2x-π\/6≤2kπ时,f(x)单调递增,此时kπ-5π\/12≤x≤k...
设函数f(x)=根号3cos^x+sinxcosx-根号3\/2
解 f(x)=√3cos²x+sinxcosx-√3\/2 =√3*(1+cos2x)\/2+(1\/2)sin2x-√3\/2 =(1\/2)sin2x+(√3\/2)cos2x =sin(2x+π\/3)∴T=π 单增区间: -π\/2+2kπ≤2x+π\/3≤π\/2+2kπ,k∈Z -5π\/6+2kπ≤2x≤π\/6+2kπ,k∈Z -5π\/12+kπ≤x≤π\/12+2kπ...
设函数f(x)=根号3cosx的平方+sinxcosx-根3\/2(1)求f(x)的最小正周期T...
f(x)=√3cos^2x+sinxcosx -√3\/2 =(√3\/2)(1+cos2x)+(1\/2)sin2x-√3\/2 =(√3\/2)cos2x+(1\/2)sin2x =sin(2x+π\/3)(1) 最小正周期T=2π\/2=π 单增区间2x+π\/3∈[2kπ-π\/2, 2kπ+π\/2]即x∈[kπ-5π\/12, kπ+π\/12](2) x∈[0, 3π] 2x+π\/3...
已知函数f(x)=根号三cos的平方x+sin xconx-二分之根号三求f(8分之...
f(x)=根号3cos^x+sinxcosx-根号3\/2 =根号3*(1+cos2x)\/2+sin2x\/2-根号3\/2 所以f(派\/8)=根号3*(1+cos派\/4)\/2+sin(派\/4)\/2-根号3\/2 =根号3*(1\/2+根号2\/4)+根号2\/4-根号3\/2 =(根号6+根号2)\/4
已知函数f(x)=根号3cosx的平方+sinxcosx-2分之根号3 求f(x)的最小正...
(1) f(x)=sinxcosx+√3cos²X-√3\/2 =sin2x\/2+√3cos2x\/2+√3\/2-√3\/2 =sin(2x+π\/3).(2) f(x)的最小正周期为π,单调增区间是2kPai-Pai\/2<=2x+Pai\/3<=2kPai+Pai\/2 即有[kPai-5Pai\/12,kPai+Pai\/12]
fx=根号3cos平方x+sinxcosx-根号3\/2
f(x)=√3cos²x+sinx cosx-√3\/2 =√3\/2(1+cos2x)+½sin2x-√3\/2 =√3\/2cos2x+½sin2x =sin(2x+π/3)画图易知角a为(2π/3)∴f(a)=sin2π=0
已知函数f(x)=√3sinx^2+sinxcosx-√3\/2
f(x)=√3sinx^2+sinxcosx-√3/2 =√3\/2(1-cos2x)+1\/2sin2x-√3\/2 =1\/2sin2x-√3\/2cos2x =sin(2x-pi\/3)因为0<x<pi/2 那么0<2x<pi -pi\/3<2x-pi\/3<2pi\/3 当2x-pi\/3=pi\/2时,f(x)取得最大值1
已知函数f(x)=√3sinxcosx-cos²x+1\/2. 一 试求函数f(x)在区间(
回答:先把函数化简 再带入去间
帮我化简一下:函数y=√3cos²x+sinxcosx-√3\/2
y=sinxcosx+根号3cos^2 x-根号3 =sin2x\/2+根3(cos^2x-1)=sin2x\/2+根3(cos2x+1)\/2-根3 =sin2xcos60+cos2xsin60-跟3\/2 =sin(2x+60)-跟3\/2 一个对称中心为 (-π\/6,-跟3\/2)也可以说是b.(5π\/6,-√3\/2)选b ...
已知函数f(x)=√3sin^2x+sinxcosx-√3\/2(x∈R)
f(x)=根号3sin^2x+sinxcosx-根号3\/2 =sinxcosx-√3\/2*(1-2sin²x)=(1\/2)sin2x-(√3\/2)cos2x =sin(2x)*cos(π\/3)-cos(2x)sin(π\/3)=sin(2x-π\/3)如0<x<Pai\/2 那么-Pai\/3<2x-Pai\/3<2Pai\/3 故有-根号3\/2<f(x)<=1 即f(x)的最大值是:1 ...