nynw.net
当前位置:首页 >> 设函数Fx等于4sinx(Cos%sinx)加3 1.当x属于(0,派... >>

设函数Fx等于4sinx(Cos%sinx)加3 1.当x属于(0,派...

f(x) = 4sinx(cosx-sinx)+3 = 4sinxcosx-4sin²x+3 = 2sin2x-2(1-cos2x)+3 = 2sin2x+2cos2x+1 = 2√2(sin2xcosπ/4+cos2xsinπ/4) + 1 = 2√2sin(2x+π/4) + 1 x∈(0,π) 2x∈(0,2π) 2x+π/4∈(π/4,9π/4) 2x+π/4∈(π/2,3π/2)时单调递减 此...

解:(1)最简单的方法是用“积化和差”公式 2sinαcosβ = sin(α+β) + sin(α-β) 原式=2×2sinxcos(x+π/3) =2 [ sin(x+x+π/3) + sin(x-x-π/3) ] = 2 [ sin(2x + π/3) + sin (-π/3) ] = 2sin(2x + π/3) - √3 显然 T= 2π/ω = 2π/2 = π ※ 此法虽然简单,但...

f(x)=4√3sinxcosx-4cos²x+1 =2√3sin(2x)-2[cos(2x)+1]+1 =2√3sin(2x)-2cos(2x) -1 =4[sin(2x)(√3/2)-cos(2x)(1/2)] -1 =4sin(2x -π/6) -1 x∈[0,π/2] 0-π/6≤2x-π/6≤2·(π/2) -π/6 -π/6≤2x-π/6≤5π/6 -1/2≤sin(2x-π/6)≤1 4×(-1/2)-1≤4sin(2x -...

题目不详

f(x)=2sinxcosx-sin²x+cos²x =sin2x+cos2x =√2sin(2x+π/4) 在[0, π]上,2x+π/4∈[π/4, 2π+π/4] 其中单调增区间为: 2x+π/4 ∈[π/4, π/2]U[3π/2,9π/4] 单调减区间: 2x+π/4 ∈[π/2, 3π/2] 即f(x)的单调增区间为:[0, π/8]U[5π/8, π] f(x)...

参考

f(x)=sinxcosx+cos 2 x= 1 2 sin2x+ 1 2 (1+cos2x)= 2 2 sin(2x+ π 4 )+ 1 2 .(1)∴f(x)的最小正周期T= 2π 2 =π(2)∵ x∈[0, π 2 ] ,∴2x+ π 4 ∈[ π 4 , 5π 4 ]∴sin(2x+ π 4 )∈[- 2 2 ,1]∴f(x)= 2 2 sin(2x+ π 4 )+ 1 2 ∈[0...

(1) f(x)=2cos平方x/2=cosx+1 g(x)=(sinx/2+cosx/2)平方=1+sinx f(pi/2-x)=cos(pi/2-x)+1=sinx+1=g(x) (2)h(x)=f(x)-g(x)=cosx-sinx=根号(2)*cos(x+pi/4) x∈[0,pi] 所以x+pi/4∈[pi/4,5pi/4] h(x)=根号(2)*cos(x+pi/4) 当x+pi/4=pi...

f(x)=sinx(根号下3cosx–sinx) =根号3sinxcosx-(sinx)^2 =根号3/2sin2x-(1-cos2x)/2 =根号3/2sin2x+1/2cos2x-1/2 =sin(2x+Pai/6)-1/2 故当x属于(0,2Pai/3)时有Pai/6

解fx=cosx(sinx+cosx)=cosxsinx+cos²x=1/2sin2x+(1+cos2x)/2 =1/2sin2x+1/2cos2x+1/2 =√2/2sin(x+π/4)+1/2 .(1)请指出f(x)的奇偶性 由f(-x))=cos(-x)sin(-x)+cos²(-x)=-cos(x)sin(x)+cos²(x)≠f(x)或-f(x) 即...

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