nynw.net
当前位置:首页 >> 已知函数F(x)=sin(2x+π3)+sin(2x%π3)+2Cos2x... >>

已知函数F(x)=sin(2x+π3)+sin(2x%π3)+2Cos2x...

(Ⅰ)f(x)=sin2xcosπ3+cos2xsinπ3+sin2xcosπ3-cos2xsinπ3+2cos2x=sin2x+cos2x=2sin(2x+π4) (4分)∴f(π4)=2sin(2?π4+π4)=2sin3π4=1.(6分)(Ⅱ)∵-π4≤x≤π4,∴-π4≤2x+π4≤3π4,∴当2x+π4=π2,即x=π8时,f(x)max=

(1)∵得f(x)=sin2xcosπ3+sinπ3cos2x+sin2xcosπ3?sinπ3cos2x+cos2x+a=sin2x+cos2x+a∴f(x)=2sin(2x+π4)+a,…(4分)由f(x)max=2+1得a=1.…(3分)(2)∵g(x)=f(x+38π)?2=?2sin2x?1,…(4分)令-π2+2kπ≤2x≤π2+2kπ,k∈Z∴?π4+kπ≤x≤π4+kπ,k∈Z∴...

(Ⅰ)∵f(x)=cos2xcosπ3+sin2xsinπ3+cos2x=12cos2x+32sin2x+cos2x=32sin2x+32cos2x=3(12sin2x+32cos2x)=3sin(2x+π3)∴f(x)的最小正周期为π.(Ⅱ)由(Ⅰ)知f(x)=3sin(2x+π3),∴当x∈[0,

(I)∵f(x)=12cos2x+32sin2x+sin2x?cos2x=12cos2x+32sin2x?cos2x=sin(2x?π6).∴函数的最小正周期T=2π2=π.由2kπ?π2≤2x?π6≤2kπ+π2,k∈Z,得2kπ?π3≤2x≤2kπ+2π3,k∈Z.即kπ?π6≤x≤kπ+π3,∴函数f(x)的单调递增区间为[kπ?π6,kπ+π3]k∈Z.(II)∵g...

(1)∵f(x)=sin2x-3cos2x=2sin(2x-π3)…4分∴f(π3)=3…6分(2)由2kπ-π2≤2x-π3≤2kπ+π2,k∈Z得:kπ-π12≤x≤kπ+5π12,k∈Z∴函数f(x)的单调递增区间为[kπ-π12,kπ+5π12],k∈Z…12分

(1)∵f(x)=cos2xcosπ3-sin2xsinπ3+1-cos2x=-sin(2x+π6)+1,由2kπ-π2≤2x+π6≤2kπ+π2(k∈Z),得:kπ-π3≤x≤kπ+π6(k∈Z),∵x∈[-π,0],∴函数的单调递减区间为[-π,-5π6]和[-π3,0],(2)∵x∈[0,π2]时,2x+π6∈[π6,7π6],∴sin(2x+π6)∈[-12,...

(1)∵f(x)=32sin2x?12cos2x?(1+cosx)…(2分)=32sin2x?32cos2x?1=3sin(2x?π3)?1,…(4分)∴函数f(x)的最小正周期T=π. …(6分)(2)由?π6<x<π3,得?2π3≤2x?π3<π3…(10分)∴由正弦函数的图象知当2x?π3=π3即x=π3时,有ymax=3×32?1=12...

(1)∵f(x)=12cos2x+32sin2x-cos2x=32sin2x-12cos2x=sin(2x-π6),令2kπ≤2x-π6≤π2+2kπ,k∈Z,则kπ?π6≤x≤π3+kπ,k∈Z;∴函数f(x)的单调递增区间是[kπ?π6,π3+kπ],k∈Z;(2)列表如下;根据表中数据,建立平面直角坐标系,画出函数在一个周期...

(1)函数f(x)=sin(2x-π3)+cos(2x-π6)+2cos2x-1=sin2xcosπ3-cos2xsinπ3+cos2xcosπ6+sin2xsinπ6+cos2x (3分)=sin2x+cos2x (4分)=2sin(2x+π4) (5分)所以函数f(x)的最小正周期T=2π2=π.(6分)(2)∵f(x)在区间[-π4,π4]上是增...

f(x)=sin2x×12+32cos2x+12sin2x?32cos2x+cos2x=sin2x+cos2x=2sin(2x+π4)(1∵0∴T=2π2=π(2)由f(x)可以看出函数f(x)的增区间为2x+π4∈[?π2+2kπ,π2+2kπ]即函数f(x)的增区间为:[-3π8+kπ,π8+kπ]k∈Z(3)∵x∈[-π4,π4]∴2x+π4∈[?π4,3π4]根...

网站首页 | 网站地图
All rights reserved Powered by www.nynw.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com