nynw.net
当前位置:首页 >> 已知函数F(x)=sin2x+2sinxsin(π2?x) +3sin2(3π2?... >>

已知函数F(x)=sin2x+2sinxsin(π2?x) +3sin2(3π2?...

(Ⅰ)化简可得f(x)=sin2x+3sinxsin(x+π2)=1?cos2x2+3sinxcosx=32sin2x-12cos2x+12=sin(2x-π6)+12,可得周期T=2π2=π;(Ⅱ)由?π2+2kπ≤2x?π6≤π2+2kπ得?π6+kπ≤x≤π3+kπ,k∈z∴函数f(x)的单调递增区间是[?π6+kπ,π3+kπ],k∈z;(Ⅲ)由x∈[0,2π...

f(x)=2sin²x+2√3sinx×sin(x+π/2) =1-cos2x+2√3sinxcosx =1-cos2x+√3sin2x =2(√3/2*sin2x-1/2*cos2x)+1 =2sin(2x-π/6)+1 最小正周期:T=2π/2=π 行家正解,不明白可以追问!祝您学习进步 满意请点击下面的【选为满意回答】按钮,O(∩_∩)O谢谢

f(x)=sinx(sinxcosπ/6+cosxsinπ/6) =sinx(sinx*√3/2+cosx*1/2) =sin²x*√3/2+sinxcosx*1/2 =√3/2*(1-cos2x)/2+1/2*(sin2x)/2 =√3/4-√3/4*cos2x+1/4*sin2x =√3/4-1/2*(√3/2*cos2x+1/2*sin2x) =√3/4-1/2*(sinπ/3cos2x+cosπ/3sin2x) =√3/4-1/2*...

f(x)=√3/2sin2x-(cosx)²-½ =√3/2sin2x-1/2cos2x-1 =sin(2x-π/6)-1 T=2π/2=π 2x-π/6在[2kπ+π/2,2kπ+3π/2]是调递减 x在[kπ+π/3,kπ+5π/6]是调递减

1、 f(x)=sinx(sinxcosπ/6+cosxsinπ/6) =√3/2*sin²x+1/2*sinxcosx =√3/2*(1-cos2x)/2+1/2*(sin2x)/2 =√3/4+1/2*(1/2*sin2x-√3/2*cos2x) =√3/4+(sin2xcosπ/3-cos2xsinπ/3) =√3/4+sin(2x-π/3) 所以T=2π/2=π 2、 0≤x≤π/2 -π/3≤2x-π/3≤2π/3 -√3...

f(x)=4sinxsin²(π/4+x/2)+cos2x-1 =4sinxsin²[(π/2+x)/2]+cos2x-1 =4sinx[1-cos(π/2+x]/2+cos2x-1 =2sinx+2sin²x+1-2sin²x-1 =2sinx ∴f(ωx)=2sinωx x∈[-π/2,2π/3]是增函数 f'(ωx)=2ωcosωx>0 ∵ω>0 ∴cosωx>0 ω·2π/3≤π/2→ω≤3/4...

f(x)= 2 sin 2 x- 3 sinx?cosx+ cos 2 x = sin 2 x- 3 sinxcosx+1 = 1-cos2x- 3 sin2x 2 +1 = 3 2 -sin(2x+ π 6 ) (1)∵ sin(2x+ π 6 )∈[-1,1] ∴ f(x)∈[ 1 2, , 5 2 ] (2)由 π 2 +2kπ≤2x+ π 6 ≤ 3π 2 +2kπ 可得, π 6 +kπ≤x ≤ 2π 3 +kπ...

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