余弦定理的公式是什么
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a^2=b^2+c^2-2bc*cosA
b^2=c^2+a^2-2ac*cosB
c^2=a^2+b^2-2ab*cosC
a/sinA=b/sinB=C/sinC=2R(\u5916\u63a5\u5706\u534a\u5f84\uff09
a^2=b^2+c^2-2bccosA
a^2=b^2+c^2-2*b*c*CosA
b^2=a^2+c^2-2*a*c*CosB
c^2=a^2+b^2-2*a*b*CosC
CosC=(a^2+b^2-c^2)/2ab
CosB=(a^2+c^2-b^2)/2ac
CosA=(c^2+b^2-a^2)/2bc
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绛旓細1銆佹寮﹀畾鐞嗭細a/sinA=b/sinB=c/sinC=2R 2銆佷綑寮﹀畾鐞嗭細cos A=(b²+c²-a²)/2bc銆傛浣欏鸡瀹氱悊鎸囨寮﹀畾鐞嗗拰浣欏鸡瀹氱悊锛屾槸鎻ず涓夎褰㈣竟瑙掑叧绯荤殑閲嶈瀹氱悊锛岀洿鎺ヨ繍鐢ㄥ畠鍙В鍐充笁瑙掑舰鐨勯棶棰橈紝鑻ュ浣欏鸡瀹氱悊鍔犱互鍙樺舰骞堕傚綋绉讳簬鍏跺畠鐭ヨ瘑锛屽垯浣跨敤璧锋潵鏇翠负鏂逛究銆佺伒娲汇傜洿瑙掍笁瑙掑舰鐨勪竴涓攼瑙掔殑...
绛旓細浣欏鸡瀹氱悊6涓叕寮忔槸cosA=(b^2+C^2-a^2)/2bC锛宑osb=(a^2+c^2-b^2)/2aC锛宑osC=(a^2+b^2-C^2)/2ab锛宑osa+cosb=2cosa+b/2cosa-b/2锛宑osa-cosb=璐2sina+b/2sina-b/2锛宑osa涔榗osb=1/2[cos锛坅+b锛+cos锛坅-b锛塢浣欏鸡瀹氱悊鐨勫惈涔 浣欏鸡瀹氱悊锛屾姘忓钩闈㈠嚑浣曞鍩烘湰瀹氱悊銆備綑寮﹀畾鐞嗘槸...
绛旓細浣欏鸡瀹氱悊鍏紡锛歝osA=锛坆²+c²-a²锛/2bc锛宑osA=閭昏竟姣旀枩杈銆備綑寮﹀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綑寮﹀畾鐞嗘ц川 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...
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 浣欏鸡瀹氱悊鏄拡瀵逛换鎰忎笁瑙掑舰鐨.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
绛旓細浣欏鸡瀹氱悊鍏紡鏄cosA=(b²+c²-a²) /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綑寮﹀畾鐞嗘槸瑙ｄ笁瑙掑舰涓殑涓涓噸瑕佸畾鐞嗭紝鍙簲鐢ㄤ簬浠ヤ笅涓夌闇姹傦細1銆佸綋宸茬煡...
绛旓細浣欏鸡瀹氱悊琛ㄨ揪寮2锛氫綑寮﹀畾鐞嗚〃杈惧紡3锛堣鍏冨舰寮忥級鍦ㄤ换鎰忊柍ABC涓紝鍋欰D鈯C 鈭燙鎵瀵圭殑杈逛负c锛屸垹B鎵瀵圭殑杈逛负b锛屸垹A鎵瀵圭殑杈逛负a 鍒欐湁BD=cosB*c锛孉D=sinB*c锛孌C=BC-BD=a-cosB*c 鏍规嵁鍕捐偂瀹氱悊鍙緱锛欰C^2=AD^2+DC^2 b^2=(sinB*c)^2+(a-cosB*c)^2 b^2=sin^2B*c^2+a^2+...
绛旓細a^2=b^2+c^2-2bccosA 宸﹁竟鏄竴鏉¤竟a锛屽彸杈圭殑浣欏鸡鏄痑瀵瑰簲鐨勮A锛屽彸杈圭殑杈归兘鏄痓鍜宑锛岃繖鏍疯鍙兘瀹规槗鐐广傛瘮濡備竴涓笁瑙掑舰ABC涓紝鈭燙锛90掳銆傚垯AB鍙仛鏂滆竟锛孉C鍙仛鈭燗鐨勯偦杈癸紝BC鍙仛鈭燗鐨勫杈癸紝鎵浠osA锛滱C/AB锛宻inA=BC/AB锛屽悓鐞哻osB锛滲C/AB锛宻inB=AC/AB銆
绛旓細涓夎褰綑寮﹀畾鐞嗗叕寮忔槸cosA=锛坆²+c²-a²锛/2bc锛宑osA=閭昏竟姣旀枩杈广傚浜庝换鎰忎笁瑙掑舰锛屼换浣曚竴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︾殑绉殑涓ゅ嶃備綑寮﹀畾鐞嗭紝娆ф皬骞抽潰鍑犱綍瀛﹀熀鏈畾鐞嗐備綑寮﹀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锛屾槸鍕捐偂瀹氱悊鍦ㄤ竴鑸...
绛旓細1銆佷綑寮﹀畾鐞嗭細cos A=(b2+c2-a2)/2bc銆2銆佹浣欏鸡瀹氱悊鎸囨寮﹀畾鐞嗗拰浣欏鸡瀹氱悊锛屾槸鎻ず涓夎褰㈣竟瑙掑叧绯荤殑閲嶈瀹氱悊锛岀洿鎺ヨ繍鐢ㄥ畠鍙В鍐充笁瑙掑舰鐨勯棶棰橈紝鑻ュ浣欏鸡瀹氱悊鍔犱互鍙樺舰骞堕傚綋绉讳簬鍏跺畠鐭ヨ瘑锛屽垯浣跨敤璧锋潵鏇翠负鏂逛究銆佺伒娲汇3銆佺洿瑙掍笁瑙掑舰鐨勪竴涓攼瑙掔殑閭昏竟鍜屾枩杈圭殑姣斿煎彨杩欎釜閿愯鐨勪綑寮﹀笺
