sin18度36度54度72度的具体值 分数表示 sin18度和tan36度分别是多少？与黄金分割比有什么联系...
\u6c42sin18\u00b0cos36\u00b0\u503c\u3002 \u7b54\u6848\u5728\u56fe\u4e2d\u4f8b\u4e00\uff0c\u7b2c\u4e00\u6b65\u5c31\u6ca1\u770b\u61c2 ...\u6c42\u8be6\u89e3\u7b2c\u4e00\u6b65\u662f\u5206\u5b50\u5206\u6bcd\u540c\u65f6\u4e58\u4ee5 2cos18' \u7136\u540e\u4f7f\u75282\u500d\u89d2\u516c\u5f0f\u4e5f\u5c31\u662f 2sin18'cos18'=sin36'
\u6700\u540e\u518d\u6b21\u4f7f\u75282\u500d\u89d2\u516c\u5f0f 2sin36'cos36'=sin72'=cos18' \u6700\u540e\u518d\u7ea6\u5206\u4e00\u4e0b\u5c31\u662f 1/4
sin18\u00b0\u22480.309,tan36\u00b0\u22480.727\uff0c\u4e0e\u9ec4\u91d1\u5206\u5272\u6bd4\u7684\u5173\u7cfb\u8868\u793a\u771f\u5fc3\u4e0d\u77e5\u9053\u3002\u671b\u91c7\u7eb3
cos36*cos72=cos36*sin18
=(1/cos18)*sin18*cos18*cos36
=(1/2cos18)*sin36*cos36
=(1/4cos18)*sin72
=1/4
：∵sin36°＝cos54°
即sin（2×18°）＝cos（3×18°）
2sin18°cos18°＝4(cos18°)^3－3cos18°
∵cos18°≠0
∴2sin18°＝4(cos18°)^2－3
整理得4(sin18°)＾2＋2sin18°－1＝0
解得sin18°＝（根号5－1）/4
绛旓細=(1/cos18)*sin18*cos18*cos36 =(1/2cos18)*sin36*cos36 =(1/4cos18)*sin72 =1/4 锛氣埖sin36掳锛漜os54掳 鍗硈in锛2脳18掳锛夛紳cos锛3脳18掳锛2sin18掳cos18掳锛4(cos18掳)^3锛3cos18掳 鈭礳os18掳鈮0 鈭2sin18掳锛4(cos18掳)^2锛3 鏁寸悊寰4(sin18掳)锛2锛2sin18掳锛1...
绛旓細涓斾笁瑙掑舰ABC鐩镐技浜庝笁瑙掑舰ABD,鐒跺悗閫氳繃姣斾緥鍏崇郴銆佷綑寮﹀畾鐞嗗氨鍙互姹傚嚭cos72掳 鏈缁堝緱鍑簊in18掳,9,cos36搴=sin54搴 浠=sin18搴锛屽埄鐢2鍊嶈鍜3鍊嶈鍏紡 1-2x^2=3x-4x^3 鍒嗚В鍥犲紡寰(x-1)(4x^2+2x-1)=0 鏄剧劧0 (x=-(鈭5+1)/4鑸嶅幓锛夋墍浠in18搴=(鈭5-1)/4,2,(鏍瑰彿5-1锛/4,1,...
绛旓細棣栧厛姹傚嚭sin18搴鐨勭簿纭兼潵 鍥犱负cos36搴=sin54搴 浠=sin18搴︼紝鍒╃敤2鍊嶈鍜3鍊嶈鍏紡 1-2x^2=3x-4x^3 鍒嗚В鍥犲紡寰(x-1)(4x^2+2x-1)=0 鏄剧劧0<x<1,4x^2+2x-1=0,x=(鈭5-1)/4 (x=-(鈭5+1)/4鑸嶅幓锛夋墍浠in18搴=(鈭5-1)/4 鍦ㄩ粍閲戜笁瑙ｅ舰涓 搴曡竟锛氳叞锛2sin18搴=(鈭5...
绛旓細鎵浠ヨ繖涓袱涓鐨勫拰鏄180搴︼紝閭ｄ箞杩欎袱涓鍒嗗埆鏄36搴﹀拰54搴銆傛墍浠ヨ彵褰㈢殑鍚勪釜鍐呰鐨勫害鏁版槸 72搴銆108搴︺72搴﹀拰108搴︺傘
绛旓細灏sin36掳=cos54掳涓よ竟鍒嗗埆鐢ㄥ嶈鍏紡灞曞紑寰2sin18掳cos18掳=4(cos18掳)^3-3cos18掳,鍗2sin18掳=4(cos18掳)^2-3,涔熷嵆4(sin18掳)^2+2sin18掳-1=0,瑙ｅ緱sin18掳=(鈭5-1)/4.C72搴锛宑杈瑰氨鏄枩杈2锛屽湴杈逛笂鍋氶珮锛屼氦鐐瑰湪涓績锛屽彲姹傚嚭涓鍗婄殑搴曡竟2*cos72锛屽啀涔樹互2 b搴旇鏄簳杈癸紝...
绛旓細鍜屽樊鍖栫Н鍏紡 sin52-sin18=2cos36sin18 鍏堜箻cos18鍐嶉櫎cos18 2cos36sin18cos18/cos18=cos36sin36/cos18=1/2sin72/cos18 sin72=cos18 鍒欏師寮=1/2
绛旓細姝ｄ簲杈瑰舰鐨勬瘡涓唴瑙掓槸(5锛2)脳180掳/5锛108掳 杩炴帴鍦嗗績鍜屼竴鏉¤竟鐨勪袱绔紝寰楀埌涓涓瓑鑵颁笁瑙掑舰锛屽叾搴曡涓108掳/2锛54掳锛岄《瑙掍负180掳锛2脳54掳锛72掳 璁炬浜旇竟褰㈢殑杈归暱涓篴锛屽鎺ュ渾鐨勫崐寰勪负r锛屽垯r锛漚/(2cos54掳)锛漚/(2sin36掳)涓嬮潰缁欏嚭sin36掳鐨勬眰娉曪細鐢变簬sin36掳锛漵in(180掳锛36掳)锛...
绛旓細(鎴栫敱姝ｅ鸡瀹氱悊锛屽緱AB/sin72º=OB/sin54º锛屽嵆AB=50sin72º/sin54º=100sin36ºcos36º/cos36º=100sin36º)鐢眘in36º=cos54º锛屽緱 2sin18ºcos18º=4cos³18º-3cos18º锛屽嵆2sin18º=4cos²...
绛旓細瑙扐 涓36搴锛岃B涓54搴锛岃C涓90搴︼紝锛1锛変互C 涓哄渾蹇冿紝CB涓哄崐寰勶紝鍦ˋB 涓婃埅鍙朎鐐癸紝涓夎褰CE鏄瓑鑵颁笁瑙掑舰锛涳紙2锛変互E 涓哄渾蹇冿紝AE涓哄崐寰勶紝鍦ˋC 涓婃埅鍙朏鐐癸紝涓夎褰EF鏄瓑鑵颁笁瑙掑舰锛涳紙3锛夎ECB=锛180-54-54锛夊害=72搴锛岃ECF=锛90-72锛夊害=18搴锛岃AEF=锛180-36-36锛夊害=18搴︼紝...
绛旓細褰撻《瑙掍负72搴︽椂锛屽簳瑙掔殑姣旀暟绛変簬180搴-72搴γ2绛変簬54搴︼紝褰撳簳瑙掍负72搴︽槸椤惰鐨勫害鏁扮瓑浜180搴-72搴γ2绛変簬36搴︿粬鐨勫彟澶栦袱涓唴瑙掑垎鍒槸54搴54搴鎴72搴36搴銆
