www.sghz.net > sinxCosy积化和差

sinxCosy积化和差

sina+sinb=2sin1/2(a+b)*cos1/2(a-b) sina-sinb=2cos1/2(a+b)*sin1/2(a-b) cosa+cosb=2cos1/2(a+b)*cos1/2(a-b) cosa-cosb=-2sin1/2(a+b)*sin1/2(a-b)

sinθ sinφ=2sin(θ/2 θ/2)cos(θ/2-φ/2) sinθ-sinφ=2cos(θ/2 φ/2)sin(θ/2-φ/2) cosθ cosφ=2cos(θ/2 φ/2)cos(θ/2-φ/2) cosθ-cosφ=-2sin(θ/2 φ/2)sin(θ/2-φ/2) sinαsinβ=-1/2[cos(α β)-cos(α-β)] cosαcosβ= 1/2[cos(α β) cos(α-β)] sinαcosβ= 1/2[sin(α β) sin(α-β)] cosαsinβ= 1/2[sin(α β)-sin(α-β)]

sinx=siny,y=2nπ+x 或y=(2n+1)π-x cosx=cosy,y=2nπ+x, y=2nπ-x tanx=tany,y=x+nπ

有关三角函数的公式和差化积 sinX+sinY=2sin[(X+Y)/2]cos[(X-Y)/2]; sinX-sinY=2cos[(X+Y)/2]sin[(X-Y)/2] cosX+cosY=2cos[(X+Y)/2]cos[(X-Y)/2] cosX-cosY=-2sin[X+Y)/2]sin[(X-Y)/2] 积化和差sinXcosY=1/2[sin(X+Y)+sin(X-Y)] cosXsinY=1/2[sin(X+Y)-sin(X-Y)]

和差化积 sinX+sinY=2sin[(X+Y)/2]cos[(X-Y)/2]; sinX-sinY=2cos[(X+Y)/2]sin[(X-Y)/2] cosX+cosY=2cos[(X+Y)/2]cos[(X-Y)/2] cosX-cosY=-2sin[X+Y)/2]sin[(X-Y)/2] 积化和差sinXcosY=1/2[sin(X+Y)+sin(X-Y)] cosXsinY=1/2[sin(X+Y)-sin(X-Y)]

cos(x+y)=cosxcosy+sinxsinycos(x-y)=cosxcosy-sinxsiny两式相减,得到cos(x+y)-cos(x-y)=2sinxsiny得到sinxsiny={con(x+y)-con(x-y)}/2

1、积化和差公式: sinαsinβ=-[cos(α+β)-cos(α-β)] cosαcosβ=[cos(α+β)+cos(α-β)] sinαcosβ=[sin(α+β)+sin(α-β)] cosαsinβ=[sin(α+β)-sin(α-β)] 积化和差公式是由正弦或余弦的和角公式与差角公式通过加减运算推导而得.其中后两个公式可合并为一个

和差化积 2sinacosb=sin(a+b)+sin(a-b) 2cosasinb=sin(a+b)-sin(a-b) ) 2cosacosb=cos(a+b)+cos(a-b) -2sinasinb=cos(a+b)-cos(a-b) sina+sinb=2sin((a+b)/2)cos((a-b)/2 cosa+cosb=2cos((a+b)/2)sin((a-b)/2) tana+tanb=sin(a+b)/cosacosb积化和差

半角公式 sin2X=2sinXcosX;cos2X=(cosX)方-(sinX)方; tan2X=2tanX/(1-(tanX)方);cos2X=1-2sinX方=2(cosX)方-1和差化积 sinX+sinY=2sin[(X+Y)/2]cos[(X-Y)/2];sinX-sinY=2cos[(X+Y)/2]sin[(X-Y)/2]cosX+cosY=2cos[(X+Y)/2]cos[(X-Y)/2]cosX-

积化和差 sina*cosb=(sin(a+b)+sin(a-b))/2 cosa*sinb=(sin(a+b)-sin(a-b))/2 cosa*cosb=(cos(a+b)+cos(a-b))/2 sina*sinb=-(cos(a+b)-cos(a-b))/2 和差化积 sinx+siny=2sin((x+y)/2)*cos((x-y)/2) sinx-siny=2cos((x+y)/2)*sin((x-y)/2) cosx+cosy=2cos((x+y)/2

网站地图

All rights reserved Powered by www.sghz.net

copyright ©right 2010-2021。
www.sghz.net内容来自网络,如有侵犯请联系客服。zhit325@qq.com