sinx-siny sinx+siny=
sinx-siny=?sinx-siny=2sin(x-y)/2*cos(x+Y)/2
\u8ba1\u7b97\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u8bbea=(x+y)/2 , b=(x\u2013y)/2
\u90a3\u4e48x=a+b\uff0c y=a\u2013b
\u6240\u4ee5
sinx\u2013siny=sin(a+b)\u2013sin(a\u2013b)
=sina*cosb+cosa*sinb\u2013 (sina*cosb\u2013cosa*sinb)
= sina*cosb+cosa*sinb\u2013sina*cosb+cosa*sinb
=2cosa*sinb
=2sin(x\u2013y)/2*cos(x+y)/2
\u6269\u5c55\u8d44\u6599\uff1a
\u548c\u89d2\u516c\u5f0f\uff1a
sin ( \u03b1 \u00b1 \u03b2 ) = sin\u03b1 \u00b7 cos\u03b2 \u00b1 cos\u03b1 \u00b7 sin\u03b2
sin ( \u03b1 + \u03b2 + \u03b3 ) = sin\u03b1 \u00b7 cos\u03b2 \u00b7 cos\u03b3 + cos\u03b1 \u00b7 sin\u03b2 \u00b7 cos\u03b3 + cos\u03b1 \u00b7 cos\u03b2 \u00b7 sin\u03b3 - sin\u03b1 \u00b7 sin\u03b2 \u00b7 sin\u03b3
cos ( \u03b1 \u00b1 \u03b2 ) = cos\u03b1 cos\u03b2 ∓ sin\u03b2 sin\u03b1
tan ( \u03b1 \u00b1 \u03b2 ) = ( tan\u03b1 \u00b1 tan\u03b2 ) / ( 1 ∓ tan\u03b1 tan\u03b2 )
sinx+siny=2sin\uff5b\uff08x+y\uff09/2\uff5dcos\uff5b\uff08x-y\uff09/2\uff5d
sinx-siny=2cos\uff5b\uff08x+y\uff09/2\uff5dsin\uff5b\uff08x-y\uff09/2\uff5d
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)]
绛旓細sinx-siny=2cos((x+y)/2)*sin((x-y)/2)銆俢osx+cosy=2cos((x+y)/2)*cos((x-y)/2)銆俢osx-cosy=-2sin((x+y)/2)*sin((x-y)/2)銆傚拰宸寲绉叕寮忕畝浠嬶細鍖呮嫭姝ｅ鸡銆佷綑寮︺佹鍒囧拰浣欏垏鐨勫拰宸寲绉叕寮忥紝鏄笁瑙掑嚱鏁颁腑鐨勪竴缁勬亽绛夊紡锛屽拰宸寲绉叕寮忓叡10缁勩傚湪搴旂敤鍜屽樊鍖栫Н鏃讹紝蹇呴』鏄...
绛旓細f(x)=sin(x)绔偣x鍜寉 sinx-siny=cos(尉)*(x-y)鈮-y
绛旓細sinx-siny=2cos[(x+y)/2]*sin[(x-y)/2]
绛旓細绗竴姝ュ厛璇佹槑: |sin(x)|鈮x| 杩欎釜鍙互鏍规嵁sin(x)鐨勫嚑浣曞畾涔夋潵璇佹槑锛寈瀵瑰簲鐨勬槸寮ч暱锛宻in(x)瀵瑰簲鐨勬槸鍨傜洿璺濈(寮﹂暱)锛屽姬闀垮ぇ浜庣瓑浜庡鸡闀匡紝浠庤屼粠鍑犱綍瀛︿笂璇佹槑鍒帮細|sin(x)|鈮x|銆傜浜屾锛屽埄鐢ㄥ拰宸寲绉叕寮忥細|sin(x)锛sin(y)| 锛 | 2cos[(x+y)/2] sin[(x-y)/2] | 鈮 | ...
绛旓細璇佹槑锛氬洜涓簒鈮爕锛屽嵆|x-y|鈮0 鎵浠ユ湁|锛sinx-siny锛/锛坸-y锛墊锛1 鍥犱负f锛坱锛=sint涓鸿繛缁彲瀵肩殑鍑芥暟銆傛牴鎹媺鏍兼湕鏃ヤ腑鍊煎畾鐞嗭紝鍦▁,y涔嬮棿鑷冲皯瀛樺湪涓涓偣m锛屼娇寰楋紙sinx-siny锛/锛坸-y锛=(sinm)'=cosm锛1锛堟敞锛氬鏋渃osm=1锛屽嵆sinx-siny=x-y锛屽彧鏈墄=0锛寉=0鎵嶆垚绔嬶級鎵浠ュ緱璇併傛媺鏍兼湕鏃ヤ腑鍊...
绛旓細璇佹槑锛氫綔涓涓崐寰勬槸1鐨勫崟浣嶅渾 鍦ㄧ涓璞￠檺锛孫A涓嶺杞村す瑙掍负x,OB涓巟杞村す瑙掍负y,涓嶅Θ璁緔>x 杩囩偣A浣淎M鍨傜洿浜嶺杞达紝杩囩偣B浣淏N鍨傜洿浜嶺杞达紝杩囩偣A浣淎K鍨傜洿浜嶣N锛屽垯 sinx=AM,siny=BN 锝sinx-siny锝=BN-AM=BN-KN=BK 锝渪-y锝=瑙扐OB=寮ч暱AB>AB 鍦ㄧ洿瑙掍笁瑙掑舰ABK涓紝AB>BK 鎵浠ワ紝锝渪-y锝>锝...
绛旓細璁緁(x)=sinx,g(x)=x;[f(x)-f(y)]/[g(x)-g(y)]=f(尉)鐨勫鏁/g(尉)鐨勫鏁 鍗筹細涓sinx-siny涓/涓▁-y涓=涓╟os尉涓ㄢ墹1 鍗筹細涓╯inx-siny涓ㄢ墹涓▁-y涓,x涓巠涓轰换鎰忓疄鏁
绛旓細Isinx-sinyI=I2cos((x+y)/2)*sin((x-y)/2)I<=I2sin((x-y)/2)I<=I2(x-y)/2I=Ix-yI
绛旓細灏唖in鍑芥暟鍦▂鐐规嘲鍕掑睍寮,鐢变簬sin鐨勪竴闃跺鏁版槸cos,浜岄樁瀵兼暟鏄-sin,鎵浠 sinx=siny+cosy(x-y)+1/2*(-sin(y+a(x-y)))*(x-y)^2 鍏朵腑a鏄竴涓粙浜0,1涔嬮棿鐨勬暟 閭ｄ箞 |(sinx-siny)/(x-y)-cosy|=1/2*|(-sin(y+a(x-y)))*(x-y)| <=1/2|x-y| ...
绛旓細璇佹槑涓嶇瓑寮弢sinx-siny|<=|x-y|(鍏朵腑x>0) 鎴戞潵绛 棣栭〉 鍦ㄩ棶 鍏ㄩ儴闂 濞变箰浼戦棽 娓告垙 鏃呮父 鏁欒偛鍩硅 閲戣瀺璐㈢粡 鍖荤枟鍋ュ悍 绉戞妧 瀹剁數鏁扮爜 鏀跨瓥娉曡 鏂囧寲鍘嗗彶 鏃跺皻缇庡 鎯呮劅蹇冪悊 姹借溅 鐢熸椿 鑱屼笟 姣嶅┐ 涓夊啘 浜掕仈缃 鐢熶骇鍒堕 鍏朵粬 鏃ユ姤 鏃ユ姤绮鹃 鏃ユ姤骞垮満 鐢ㄦ埛 璁よ瘉...
