余弦定理的公式是什么？ 余弦定理的公式是怎样的
\u4f59\u5f26\u5b9a\u7406\u516c\u5f0f\u662f\u4ec0\u4e48\uff1f\u4f59\u5f26\u5b9a\u7406\u8868\u8fbe\u5f0f1\uff1a
\u540c\u7406\uff0c\u4e5f\u53ef\u63cf\u8ff0\u4e3a\uff1a
\u4f59\u5f26\u5b9a\u7406\u8868\u8fbe\u5f0f2\uff1a
\u4f59\u5f26\u5b9a\u7406\u8868\u8fbe\u5f0f3\uff08\u89d2\u5143\u5f62\u5f0f\uff09
\u6269\u5c55\u8d44\u6599\uff1a\u4f59\u5f26\u5b9a\u7406\u8bc1\u660e\uff1a
1\u3001\u5e73\u9762\u4e09\u89d2\u5f62\u8bc1\u6cd5
\u5728\u25b3ABC\u4e2d\uff0cBC=a\uff0cAC=b\uff0cAB=c\uff0c\u4f5cAD\u22a5BC\u4e8eD\uff0c\u5219AD=c*sinB\uff0cDC=a-BD=a-c*cosB
\u5728Rt\u25b3ACD\u4e2d\uff0c
b²=AD²+DC²=\uff08c*sinB\uff09²+\uff08a-c*cosB\uff09²
=c²sin²B+a²-2ac*cosB+c²cos²B
=c²\uff08sin²B+cos²B\uff09+a²-2ac*cosB
=c²+a²-2ac*cosB
2\u3001\u5e73\u9762\u5411\u91cf\u8bc1\u6cd5
\u6709a+b=c\uff08\u5e73\u884c\u56db\u8fb9\u5f62\u5b9a\u5219\uff1a\u4e24\u4e2a\u90bb\u8fb9\u4e4b\u95f4\u7684\u5bf9\u89d2\u7ebf\u4ee3\u8868\u4e24\u4e2a\u90bb\u8fb9\u5927\u5c0f\uff09
\u2234c\u00b7c=\uff08a+b\uff09\u00b7\uff08a+b\uff09
\u2234c²=a\u00b7a+2a\u00b7b+b\u00b7b\u2234c²=a²+b²+2|a||b|cos\uff08\u03c0-\u03b8\uff09
\u53c8\u2235cos\uff08\u03c0-\u03b8\uff09=-cos\u03b8\uff08\u8bf1\u5bfc\u516c\u5f0f\uff09
\u2234c²=a²+b²-2|a||b|cos\u03b8
\u6b64\u5373c²=a²+b²-2abcosC
\u5373cosC=\uff08a2+b2-c2\uff09/2*a*b
\u4f59\u5f26\u5b9a\u7406\u662f\u63ed\u793a\u4e09\u89d2\u5f62\u8fb9\u89d2\u5173\u7cfb\u7684\u91cd\u8981\u5b9a\u7406\uff0c\u76f4\u63a5\u8fd0\u7528\u5b83\u53ef\u89e3\u51b3\u4e00\u7c7b\u5df2\u77e5\u4e09\u89d2\u5f62\u4e24\u8fb9\u53ca\u5939\u89d2\u6c42\u7b2c\u4e09\u8fb9\u6216\u8005\u662f\u5df2\u77e5\u4e09\u4e2a\u8fb9\u6c42\u89d2\u7684\u95ee\u9898\uff0c\u82e5\u5bf9\u4f59\u5f26\u5b9a\u7406\u52a0\u4ee5\u53d8\u5f62\u5e76\u9002\u5f53\u79fb\u4e8e\u5176\u5b83\u77e5\u8bc6\uff0c\u5219\u4f7f\u7528\u8d77\u6765\u66f4\u4e3a\u65b9\u4fbf\u3001\u7075\u6d3b\u3002
\u3000\u3000\u5bf9\u4e8e\u4efb\u610f\u4e09\u89d2\u5f62
\u4e09\u8fb9\u4e3aa,b,c
\u4e09\u89d2\u4e3aa,b,c
\u6ee1\u8db3\u6027\u8d28
\u3000\u3000(\u6ce8\uff1aa*b\u3001a*c\u5c31\u662fa\u4e58b\u3001a\u4e58c
\u3002a^2\u3001b^2\u3001c^2\u5c31\u662fa\u7684\u5e73\u65b9\uff0cb\u7684\u5e73\u65b9\uff0cc\u7684\u5e73\u65b9\u3002)
\u3000\u3000a^2=b^2+c^2-2*b*c*cosa
\u3000\u3000b^2=a^2+c^2-2*a*c*cosb
\u3000\u3000c^2=a^2+b^2-2*a*b*cosc
\u3000\u3000cosc=(a^2+b^2-c^2)/2ab
\u3000\u3000cosb=(a^2+c^2-b^2)/2ac
\u3000\u3000cosa=(c^2+b^2-a^2)/2bc
\u3000\u3000\u8bc1\u660e\uff1a
\u3000\u3000\u2235\u5982\u56fe\uff0c\u6709a+b=c
\u3000\u3000\u2234c\u00b7c=(a+b)\u00b7(a+b)
\u3000\u3000\u2234c^2=a\u00b7a+2a\u00b7b+b\u00b7b\u2234c^2=a^2+b^2+2|a||b|cos(\u03c0-\u03b8)
\u3000\u3000\u6574\u7406\u5f97\u5230c^2=a^2+b^2-2|a||b|cos\u03b8\uff08\u6ce8\u610f\uff1a\u8fd9\u91cc\u7528\u5230\u4e86\u4e09\u89d2\u51fd\u6570\u516c\u5f0f\uff09
\u3000\u3000\u518d\u62c6\u5f00\uff0c\u5f97c^2=a^2+b^2-2*a*b*cosc
\u3000\u3000\u540c\u7406\u53ef\u8bc1\u5176\u4ed6\uff0c\u800c\u4e0b\u9762\u7684cosc=(c^2-b^2-a^2)/2ab\u5c31\u662f\u5c06cosc\u79fb\u5230\u5de6\u8fb9\u8868\u793a\u4e00\u4e0b\u3002
\u3000\u3000---------------------------------------------------------------------------------------------------------------
\u3000\u3000\u5e73\u9762\u51e0\u4f55\u8bc1\u6cd5\uff1a
\u3000\u3000\u5728\u4efb\u610f\u25b3abc\u4e2d
\u3000\u3000\u505aad\u22a5bc.
\u3000\u3000\u2220c\u6240\u5bf9\u7684\u8fb9\u4e3ac\uff0c\u2220b\u6240\u5bf9\u7684\u8fb9\u4e3ab\uff0c\u2220a\u6240\u5bf9\u7684\u8fb9\u4e3aa
\u3000\u3000\u5219\u6709bd=cosb*c\uff0cad=sinb*c\uff0cdc=bc-bd=a-cosb*c
\u3000\u3000\u6839\u636e\u52fe\u80a1\u5b9a\u7406\u53ef\u5f97\uff1a
\u3000\u3000ac^2=ad^2+dc^2
\u3000\u3000b^2=(sinb*c)^2+(a-cosb*c)^2
\u3000\u3000b^2=sin^2b*c^2+a^2+cos^2b*c^2-2ac*cosb
\u3000\u3000b^2=(sin^2b+cos^2b)*c^2-2ac*cosb+a^2
\u3000\u3000b^2=c^2+a^2-2ac*cosb
\u3000\u3000cosb=(c^2+a^2-b^2)/2ac
\u3000\u3000\u4ece\u4f59\u5f26\u5b9a\u7406\u548c\u4f59\u5f26\u51fd\u6570\u7684\u6027\u8d28\u53ef\u4ee5\u770b\u51fa\uff0c\u5982\u679c\u4e00\u4e2a\u4e09\u89d2\u5f62\u4e24\u8fb9\u7684\u5e73\u65b9\u548c\u7b49\u4e8e\u7b2c\u4e09\u8fb9\u7684\u5e73\u65b9\uff0c\u90a3\u4e48\u7b2c\u4e09\u8fb9\u6240\u5bf9\u7684\u89d2\u4e00\u5b9a\u662f\u76f4\u89d2\uff0c\u5982\u679c\u5c0f\u4e8e\u7b2c\u4e09\u8fb9\u7684\u5e73\u65b9\uff0c\u90a3\u4e48\u7b2c\u4e09\u8fb9\u6240\u5bf9\u7684\u89d2\u662f\u949d\u89d2\uff0c\u5982\u679c\u5927\u4e8e\u7b2c\u4e09\u8fb9\u7684\u5e73\u65b9\uff0c\u90a3\u4e48\u7b2c\u4e09\u8fb9\u6240\u5bf9\u7684\u89d2\u662f\u9510\u89d2\u3002\u5373\uff0c\u5229\u7528\u4f59\u5f26\u5b9a\u7406\uff0c\u53ef\u4ee5\u5224\u65ad\u4e09\u89d2\u5f62\u5f62\u72b6\u3002\u540c\u65f6\uff0c\u8fd8\u53ef\u4ee5\u7528\u4f59\u5f26\u5b9a\u7406\u6c42\u4e09\u89d2\u5f62\u8fb9\u957f\u53d6\u503c\u8303\u56f4\u3002
余弦的积的2倍。
绛旓細鍦ㄧ洿瑙掍笁瑙掑舰涓,涓涓攼瑙掔殑浣欏鸡锛濆畠鐨勯偦杈 / 鏂滆竟,涓涓攼瑙掔殑姝ｅ鸡锛濆畠鐨勫杈 / 鏂滆竟 姣斿涓涓笁瑙掑舰ABC涓,鈭燙锛90掳.鍒橝B鍙仛鏂滆竟,AC鍙仛鈭燗鐨勯偦杈,BC鍙仛鈭燗鐨勫杈.鎵浠,cosA锛滱C/AB,sinA=BC/AB.鍚岀悊cosB锛滲C/AB,sinB=AC/AB 浣欏鸡瀹氱悊鏄閽堝浠绘剰涓夎褰㈢殑.姣斿涓夎褰BC涓,濡傛灉鈭燗,鈭燘...
绛旓細浣欏鸡瀹氱悊琛ㄨ揪寮1锛氬悓鐞嗭紝涔熷彲鎻忚堪涓猴細浣欏鸡瀹氱悊琛ㄨ揪寮2锛氫綑寮﹀畾鐞嗚〃杈惧紡3锛堣鍏冨舰寮忥級
绛旓細鍥炵瓟锛歛 2 = b 2 + c 2 -2 bccosA , 2 2 2 cos 2 b c a A bc
绛旓細姝浣欏鸡瀹氱悊鍏紡澶у叏濡備笅锛氭寮﹀畾鐞嗘帹璁哄叕寮忥細1銆侊紙1锛塧=2RsinA锛涳紙2锛塨=2RsinB锛涳紙3锛塩=2RsinC銆2銆侊紙1锛塧:b=sinA:sinB锛涳紙2锛塧:c=sinA:sinC锛涳紙3锛塨:c=sinB:sinC锛涳紙4锛塧:b:c=sinA:sinB:sinC銆3銆佺敱鈥渁/sinA=b/sinB=c/sinC=2R鈥濆彲寰楋細锛1锛(a+b)/(sinA+sinB)=2R锛涳紙2...
绛旓細浣欏鸡瀹氱悊鍏紡锛歝osA=锛坆²+c²-a²锛/2bc锛宑osA=閭昏竟姣旀枩杈广備綑寮﹀畾鐞嗘槸鎻忚堪涓夎褰腑涓夎竟闀垮害涓庝竴涓鐨勪綑寮﹀煎叧绯荤殑鏁板瀹氱悊銆傝繍鐢ㄥ畠鍙В鍐充竴绫诲凡鐭ヤ笁瑙掑舰涓よ竟鍙婂す瑙掓眰绗笁杈规垨鑰呮槸宸茬煡涓変釜杈规眰瑙掔殑闂銆備笁瑙掑舰浣欏鸡瀹氱悊鐨勫叕寮瀵逛簬杈归暱涓篴銆乥銆乧鑰岀浉搴旇涓篈銆丅銆丆鐨勪笁瑙掑舰锛屾湁...
绛旓細鍗婅鍏紡锛歝os(A/2)=卤鈭氾紙锛1+cosA)/2)鍊嶈鍏紡锛欳os2A=CosA^2-SinA^2=1-2SinA^2=2CosA^2-1 涓よ鍜屼笌宸叕寮忥細cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB 绉寲鍜屽樊鍏紡锛歝osAcosB=/2 cosAsinB=/2 鍜屽樊鍖栫Н鍏紡锛歝osA+cosB=2coscos cosA-cosB=-2sinsin 浣欏鸡瀹氱悊...
绛旓細3. 鐭ヨ瘑鐐逛緥棰樿瑙ｏ細鍋囪鎴戜滑鏈変竴涓笁瑙掑舰ABC锛岃竟闀垮垎鍒负a銆乥銆乧锛岃A銆佽B銆佽C鍒嗗埆瀵瑰簲杈筧銆乥銆乧.渚嬮锛氬凡鐭ヤ竴涓笁瑙掑舰鐨勪袱鏉¤竟杈归暱鍒嗗埆涓篴=5cm锛宐=7cm锛屽す瑙扖鐨勫害鏁颁负30掳锛屾眰绗笁鏉¤竟c鐨勯暱搴︺傝В绛旇繃绋嬶細鏍规嵁cos浣欏鸡瀹氱悊鍏紡锛歝² = a² + b² - 2ab路cos(C)浠...
绛旓細瀵逛簬浠绘剰涓夎褰BC锛屽鏋滆鈭燗銆佲垹B銆佲垹C鐨勫杈瑰垎鍒负a銆乥銆乧锛岄偅涔浣欏鸡瀹氱悊琛ㄨ揪涓猴細a² = b² + c² - 2bc*cosA锛宐² = a² + c² - 2ac*cosB锛宑² = a² + b² - 2ab*cosC銆傝繖浜鍏紡灞曠ず浜嗕笁瑙掑舰杈归暱鍜屽搴斿唴瑙掍綑寮﹀间箣闂寸殑...
绛旓細浣欏鸡瀹氱悊鏄鎸囷細瀵逛簬浠绘剰涓夎褰紝浠讳綍涓杈圭殑骞虫柟绛変簬鍏朵粬涓よ竟骞虫柟鐨勫拰鍑忓幓杩欎袱杈逛笌瀹冧滑澶硅鐨勪綑寮︾殑绉殑涓ゅ嶏紝鍗: cos A=(b+c-a)/2bc銆傜浉鍏充粙缁嶏細鍘嗗彶涓婏紝姝ｅ鸡瀹氱悊鐨鍑犱綍鎺ㄥ鏂规硶涓板瘜澶氬僵銆傛牴鎹叾鎬濊矾鐗瑰緛锛屼富瑕佸彲浠ュ垎涓轰袱绉嶃傜涓绉嶆柟娉曞彲浠ョО涓 鈥滃悓寰勬硶 鈥濓紝鏈鏃╀负13涓栫邯闃挎媺浼暟瀛﹀銆佸ぉ鏂囧瀹剁撼...
绛旓細1. 姝ｅ鸡瀹氱悊:A / Sina = B / SINB = C / sinc = 2R銆2. 浣欏鸡瀹氱悊:cos a = (b²+ c²- a²)/ 2bc銆3.姝ｅ鸡浣欏鸡瀹氱悊鏄鎸囨寮﹀畾鐞嗗拰浣欏鸡瀹氱悊銆傚畠鏄彮绀轰笁瑙掑舰杈逛笌瑙掍箣闂村叧绯荤殑涓涓噸瑕佸畾鐞嗐傚畠鍙互鐩存帴鐢ㄤ簬姹傝В涓夎褰㈤棶棰樸傚鏋滃皢浣欏鸡瀹氱悊杩涜鍙樺舰锛屽苟閫傚綋鍦拌浆绉诲埌鍏朵粬鐭ヨ瘑...
