nynw.net
当前位置:首页 >> 已知函数F(x)=3sin2x+sinxCosx?32(x∈R).(1)若x... >>

已知函数F(x)=3sin2x+sinxCosx?32(x∈R).(1)若x...

f(x)=2cosxcos(x?π6)?3sin2x+sinxcosx=2cosx(32cosx+12sinx)-3sin2x+sinxcosx=3(cos2x-sin2x)+2sinxcosx=3cos2x+sin2x=2(32cos2x+12sin2x)=2sin(2x+π3),(1)∵ω=2,∴T=2π2=π;(2)∵f(x)=1,即2sin(2x+π3)=1,∴sin(2x+π3)=12,...

x=sin(2x+π/6)+cos²x+√3sinxcosx =√3/2sin2x+1/2cos2x+1/2(cos2x+1)+√3/2sin2x =√3sin2x+cos2x+1/2 =2sin(2x+π/6)+1/2 |x|

2x+π/3∈(π/3,4π/3) 2x+π/3看成一个整体a.取值a∈(π/3,4π/3) sin a (-√3/2,1]就是个sin的函数. 所以sin(2x+π/3)∈(-√3/2,1]

f'(x)=1/2cos2x*(2x)]+cosx =cos2x+cosx 显然这是偶函数 cos2x+cosx =2cos²x-1+cosx =2(cosx+1/4)²-9/8 -1

f(x)=√3sinxcosx+cos²x =(√3/2)·2sinxcosx+½(2cos²x-1)+½ =(√3/2)sin2x+½cos2x+½ =sin(2x+π/6) +½ 最小正周期T=2π/2=π

解: (1) f(x)=cos²x-√3sinxcosx+½ =½[1+cos(2x)]-(√3/2)sin(2x)+½ =½cos(2x)-(√3/2)sin(2x)+1 =cos(2x+π/3)+1 最小正周期T=2π/2=π cos(2x+π/3)=1时,f(x)取得最大值f(x)max=1+1=2 cos(2x+π/3)=-1时,f(x)取得最小值f(...

(1)g(x)=2sin2x+sin2x-1=sin2x-cos2x=2sin(2x?π4)先将f(x)的图象向右平移π4个单位长度得到y=sin(x?π4)的图象;再将y=sin(x?π4)图象上各点的横坐标变为原来的12倍,得到函数y=sin(2x?π4)的图象;最后将曲线上各点的纵坐标变为原来的2倍...

(Ⅰ)∵f(x)=sinxcosx+sin2x,∴f(π4)=sinπ4cosπ4+sin2π4,…(1分)=(22)2+(22)2 …(4分)=1.…(6分)(Ⅱ)f(x)=sinxcosx+sin2x=12sin2x+1?cos2x2,…(8分)=12(sin2x?cos2x)+12=22sin(2x?π4)+12,…(9分)由x∈[0,π2]得 2x?π4∈[?π4,3π4],...

f(x)=sin^2x+√3sinxcosx+2cos^2x =cos^2x+√3/2*2sinxcosx+1 =1/2cos2x+√3/2sin2x+3/2 =sinx(2x+π/6)+3/2 T=2π/2=π 2x+π/6在[2kπ-π/2,2kπ+π/2]上单调递增 x在[kπ-5π/12,kπ+π/6]上单调递增 2)y=sin2x的图像经X轴向左平移π/12个单位得到y=sinx(2x+...

求到2x+π/3∈[π/3,4π/3]这一步 2x+π/3=π时,sin最大=1 2x+π/3=4π/3时,sin最小=-√3/2

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