三角形abc的内角abc的对边分别为abc在三角形abc中内角abc的对边分别为abc
关于三角形abc的内角abc的对边分别为abc,在三角形abc中内角abc的对边分别为abc这个很多人还不知道,今天来为大家解答以上的问题,现在让我们一起来看看吧!1、(1)因为(cosA-2cosC)÷cosB=(2c-a)÷b 根据正弦定理(cosA-2cosC)÷cosB=(sinA-2sinC)÷sinB因为cosB=-cos(A+C)sinB=sin(A+C)所以(cosA-2cosC)÷-cos(A+C)=(sinA-2sinC)÷sin(A+C)cosA-2cosC)÷(sinAsinC-cosCcosA)=(sinA-2sinC)÷(sinAcosC+sinCsinA)化简可得sinC=2sinA即sinC÷sinA=2=c/a。
绛旓細鍏充簬涓夎褰bc鐨勫唴瑙抋bc鐨勫杈鍒嗗埆涓篴bc锛屽湪涓夎褰bc涓唴瑙抋bc鐨勫杈瑰垎鍒负abc杩欎釜寰堝浜鸿繕涓嶇煡閬擄紝浠婂ぉ鏉ヤ负澶у瑙g瓟浠ヤ笂鐨勯棶棰橈紝鐜板湪璁╂垜浠竴璧锋潵鐪嬬湅鍚э紒1銆(1)鍥犱负锛坈osA-2cosC锛壝穋osB=锛2c-a锛壝穊 鏍规嵁姝e鸡瀹氱悊锛坈osA-2cosC锛壝穋osB=锛坰inA-2sinC锛壝穝inB鍥犱负cosB=-cos锛圓+C锛塻inB=sin...
绛旓細bc ac ab
绛旓細瑙o細鈻ABC鐨闈㈢Н涓篴^2/(3sinA)=(1/2)bcsinA,鐢辨寮﹀畾鐞嗭紝sinBsinC=2/3锛屸憼 6cosBcosC=1锛宑osBcosC=1/6,鈶 鈶-鈶犲緱cos(B+C)=1/6-2/3=-1/2锛宑osA=1/2,sinA=鈭3/2锛屸憽骞虫柟寰(1-sin^B)(1-sin^C)=1/36,鈭1-sin^B-sin^C+sin^BsinC=1/36,鐢扁憼锛宻in^B+sin^C=1+4...
绛旓細锛1锛夈佺敱姝e鸡瀹氱悊锛歛/sinA=b/sinB=c/sinC=2R锛屸斺斻(2c-a)/b=(4RsinC-2RsinA)/2RsinB=(2sinC-sinA)/sinB=(cosA-2cosC)/cosB锛屸斺斻媍osB(2sinC-sinA)=sinB(cosA-2cosC)锛屸斺斻2(cosBsinC+sinBcosC)=cosAsinB+sinAcosB锛屸斺斻2sin(B+C)=2sinA=sin(A+B)=sinC锛屸斺斻媠...
绛旓細鎵浠inC/c=sinA/a=sinC/鈭2=(鈭2/2)/2锛宻inC=1/2锛屸柍ABC锛孉=3鈭/4锛屾墍浠=鈭/6銆傚悓瑙涓夎鍑芥暟 锛1锛夊钩鏂瑰叧绯伙細sin^2(伪)+cos^2(伪)=1 tan^2(伪)+1=sec^2(伪)cot^2(伪)+1=csc^2(伪)锛2锛夌Н鐨勫叧绯伙細sin伪=tan伪*cos伪 cos伪=cot伪*sin伪 tan伪=sin伪*sec伪 cot伪...
绛旓細(b+c)/a=cosC+鈭3sin C 姝e鸡瀹氱悊浠e叆锛氾紙sinB+sinC锛/sinA=cosC+鈭3sin C sin(A+C)+sinC=sinA(cosC+鈭3sin C)sinAcosC+cosAsinC+sinC=sinAcosC+鈭3sinAsinC cosAsinC+sinC=鈭3sinAsinC sinC鈮0锛岀害鍘伙細cosA+1=鈭3sinA 鈭3sinA-cosA=1 鈭3/2.sinA-1/2.cosA=1/2 sinAcos螤/6-...
绛旓細A+B-C=蟺-2C,B+C=蟺-A,鎵浠sin(A+B-C)=csin(B+C)鍙樹负 asin(2C)=csinA,鐢辨寮﹀畾鐞嗭紝sinAsin(2C)=sinAsinC,涓よ竟閮介櫎浠2sinAsinC,寰梒osC=1/2,鎵浠=蟺/3.
绛旓細瑙o細b/sinB=a/sinA 锛2鈭3锛/锛堚垰3/2锛=2/sinA sinA=1/2 A=30掳 B=60掳 C=180掳-30掳-60掳=90掳 c/sinC=b/sinB c=锛坆sinC锛/sinB c=2鈭3x1/锛堚垰3/2锛塩=4 绛旀姝g‘锛岀浖閲囩撼锛岄潪甯告劅璋備翰锛岃銆愰噰绾崇瓟妗堛戯紝鎮ㄧ殑閲囩撼鏄垜绛旈鐨勫姩鍔涳紝璋㈣阿銆
绛旓細濡備笂鍥炬墍绀恒
绛旓細2bcosC=2a+c 鐢辨寮﹀畾鐞:a/sinA=b/sinB=c/sinC 鍒 2sinBcosC=2sinA+sinC A+B+C=蟺 鍒橝=蟺-(B+C)甯﹀叆锛2sinBcosC=2sin(B+C)+sinC=2sinBcosC+2cosBsinC+sinC 鍒欙細 2cosBsinC+sinC=0 鍥犱负C鈮0锛屽垯sinC鈮0锛 鍒 cosB=-1/2锛屽垯B=120掳 ~~~寤堕暱D鑷矱,浣垮緱DE=BD,杩炴帴AE 鍥犱负...