在三角行内sin18度等于多少啊 ??? sin18度等于多少？
sin18\u5ea6\u7b49\u4e8e\u591a\u5c11\u600e\u4e48\u8ba1\u7b97\uff1f\u8c22\u8c22\u89e3\u6cd51.\u4ee4x = 18\u00b0
\u2234cos3x = sin2x
\u22344(cosx)^3 - 3cosx = 2sinxcosx
\u2235cosx\u2260 0
\u22344(cosx)^2 - 3 = 2sinx
\u22344sinx2 + 2sinx - 1 = 0,
\u53c80 < sinx < 1
\u2234sinx = (\u221a5 - 1)/4
\u5373sin18\u00b0 = (\u221a5 - 1)/4.
\u89e3\u6cd52. \u4f5c\u9876\u89d2\u4e3a36\u00b0\u3001\u8170\u957f\u4e3a1 \u7684\u7b49\u8170\u4e09\u89d2\u5f62ABC, BD\u4e3a\u5176\u5e95\u89d2B\u7684\u5e73\u5206\u7ebf\uff0c\u8bbeAD = x
\u5219AD = BD = BC = x, DC = 1 - x.
\u7531\u76f8\u4f3c\u4e09\u89d2\u5f62\u5f97\uff1ax2 = 1 - x
\u2234x = (\u221a 5 - 1)/2
\u2234sin18\u00b0 = x/2 = (\u221a5 - 1)/4.
\u89e3\uff1a\u2235sin36\u00b0\uff1dcos54\u00b0
\u5373sin\uff082\u00d718\u00b0\uff09\uff1dcos\uff083\u00d718\u00b0\uff09
2sin18\u00b0cos18\u00b0\uff1d4(cos18\u00b0)^3\uff0d3cos18\u00b0
\u2235cos18\u00b0\u22600
\u22342sin18\u00b0\uff1d4(cos18\u00b0)^2\uff0d3
\u6574\u7406\u5f974(sin18\u00b0)\uff3e2\uff0b2sin18\u00b0\uff0d1\uff1d0
\u89e3\u5f97sin18\u00b0\uff1d\uff08\u6839\u53f75\uff0d1\uff09/4
\u6b63\u5f26\u51fd\u6570
\u4e00\u822c\u7684\uff0c\u5728\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0c\u7ed9\u5b9a\u5355\u4f4d\u5706\uff0c\u5bf9\u4efb\u610f\u89d2\u03b1\uff0c\u4f7f\u89d2\u03b1\u7684\u9876\u70b9\u4e0e\u539f\u70b9\u91cd\u5408\uff0c\u59cb\u8fb9\u4e0ex\u8f74\u975e\u8d1f\u534a\u8f74\u91cd\u5408\uff0c\u7ec8\u8fb9\u4e0e\u5355\u4f4d\u5706\u4ea4\u4e8e\u70b9P\uff08u\uff0cv\uff09\uff0c\u90a3\u4e48\u70b9P\u7684\u7eb5\u5750\u6807v\u53eb\u505a\u89d2\u03b1\u7684\u6b63\u5f26\u51fd\u6570\uff0c\u8bb0\u4f5cv=sin\u03b1\u3002\u901a\u5e38\uff0c\u6211\u4eec\u7528x\u8868\u793a\u81ea\u53d8\u91cf\uff0c\u5373x\u8868\u793a\u89d2\u7684\u5927\u5c0f\uff0c\u7528y\u8868\u793a\u51fd\u6570\u503c\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u5b9a\u4e49\u4e86\u4efb\u610f\u89d2\u7684\u4e09\u89d2\u51fd\u6570y=sin x\uff0c\u5b83\u7684\u5b9a\u4e49\u57df\u4e3a\u5168\u4f53\u5b9e\u6570\uff0c\u503c\u57df\u4e3a[-1,1]\u3002
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
sin18度=(根号5-1)/4
cos18度=(根号(10+2根号5))/4
tan18度=根号((5-2根号5)/5)
cot18度=根号(5+2根号5)
sec18度=根号((10-2根号5)/5)
csc18度=根号5+1
sin18度=(根号5-1)/4
cos18度=(根号(10+2根号5))/4
tan18度=根号((5-2根号5)/5)
cot18度=根号(5+2根号5)
sec18度=根号((10-2根号5)/5)
csc18度=根号5+1
解：∵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
sin18=（根号5-1）/4
绛旓細sin18=0.309016994 cos36=0.809016994
绛旓細涓銆10鍒360搴︿笁瑙鍑芥暟鍊艰〃 浜屻佸弽涓夎鍑芥暟鍊艰〃 涓夎鍑芥暟 1銆佸父瑙佺殑涓夎鍑芥暟鍖呮嫭姝ｅ鸡鍑芥暟銆佷綑寮﹀嚱鏁板拰姝ｅ垏鍑芥暟銆傚湪鑸捣瀛︺佹祴缁樺銆佸伐绋嬪绛夊叾浠栧绉戜腑锛岃繕浼氱敤鍒板浣欏垏鍑芥暟銆佹鍓插嚱鏁般佷綑鍓插嚱鏁般佹鐭㈠嚱鏁般佷綑鐭㈠嚱鏁般佸崐姝ｇ煝鍑芥暟銆佸崐浣欑煝鍑芥暟绛夊叾浠栫殑涓夎鍑芥暟銆2銆佷笉鍚岀殑涓夎鍑芥暟涔嬮棿鐨勫叧绯诲彲浠ラ氳繃...
绛旓細鐒跺悗锛屾垜浠彲浠ラ氳繃鍑犱綍鏂规硶鏉ユ眰瑙ｃ傚湪鍧愭爣绯涓鐢诲嚭鍗曚綅鍦嗭紝鎵惧埌涓巟杞存鍗婅酱鎴18掳瑙掔殑鐐笴锛孋鐐圭殑绾靛潗鏍囧嵆涓簊in18掳鐨勫笺傜劧鑰岋紝杩欑鏂规硶鍦ㄧ焊涓婃搷浣滃彲鑳戒細鏈夎宸紝闇瑕佺粏蹇冩搷浣溿傚浜庢洿绮剧‘鐨勫硷紝浠ｆ暟娉曠櫥鍦恒傛垜浠煡閬18掳绛変簬蟺/10寮у害锛岄氳繃涓夎鎭掔瓑寮忥紝鎴戜滑鍙互鎺ㄥ鍑簊in18掳鐨勭簿纭笺備緥濡傦紝鍒╃敤...
绛旓細鈫3sin18掳-4sin³18掳锛1-2sin²18掳 鈫4sin³18掳-2sin²18掳-3sin18掳+1锛0 鈫(sin18掳-1)(4sin²18掳+2sin18掳-1)锛0.鏄剧劧锛宻in18掳鈮1,鍗硈in18掳-1鈮0,鏁 4sin²18掳+2sin18掳-1锛0 鈭磗in18掳锛(-1+鈭5)/4 (鍙︿竴鏍逛负璐燂紝鑸)
绛旓細璁＄畻锛歵an 18搴︾瓑浜庡灏锛堣鏈夊嚑鍒嗕箣鏍瑰彿鍑犵殑鍒嗘暟锛夛紵
绛旓細瑙ｅ緱a1=(1+鈭5)b/2锛宎2=(1涓鈭5)b/2(涓嶅悎棰樻剰鑸嶅幓)銆侫B=(鈭5+1)BC/2銆傚欢闀緽A鑷矱锛屼娇AE=AC锛岃繛鎺C 鍒<AEC=<ACE=18搴锛<ECB=<ECA+<ABC=72搴+18搴=90搴 杩嘇鐐逛綔AF//BC锛屼氦EC浜嶧蹇呭钩鍒咵C锛孉F=BC/2=b/2 鍒涓夎褰EAF涓Rt涓夎褰紝<EFA=<ECB=90搴 鍦≧t涓夎褰FA涓:s鈪...
绛旓細/BC 瑙ｅ緱BC=锛堚垰5-1锛/2*AC 鍋欰H鈯C浜嶩锛屽垯鈭燞AC=18锛孒C=BC/2=锛堚垰5-1锛/4*AC sin18=sinHAC=HC/AC=锛堚垰5-1锛/4 琛ュ厖锛5X²-15X-AX+3A=0 锛坸-3锛夛紙5x-A锛=0 涓ゆ牴涓簒1=3锛寈2=A/5 鍥犱负sinA<1 sinA=A/5 sinB/B=sinA/A=1/5锛宻inB=1锛岃B涓虹洿瑙掞紝A=4 ...
绛旓細鎵浠モ垹A=鈭燗BD=36掳锛屸垹BDC=鈭燙=72掳锛屾墍浠D=BD=BC=x锛屸柍ABC鈭解柍BCD锛寉/x=x/(y-x锛,x²=y²-xy锛屼袱杈归兘闄や互x²寰楋紝(y/x)²-y/x-1=0锛寈鍒嗕箣y鐨勫涓锛1+鈭5锛/2锛岃繃A浣淎E鈯C浜嶦锛屽垯鈭燛AC=18掳 sin18搴=CE/AC=(x/2)/y=x/2y=(鈭5-1)/4 ...
绛旓細浣滀竴涓《瑙36搴,搴曡72搴︾殑绛夎叞涓夎褰ABC,銆圓=36搴,銆圔=銆圕=72搴,浣溿圔骞冲垎绾緽D,浜C浜嶥,鍒欎笁瑙掑舰BDC鐩镐技浜庝笁瑙掑舰ABC,璁綜D=x,璁綛C=1,BD=BC=AD=1,BC/AC=CD/BC,(1+x)*x=1,x=(鈭5-1锛/2,AC=CD+AD=(鈭5+1锛/2,浣淎E鈯C,鍨傝冻E,銆圗AC=18搴,sin18掳=CE/AC=锛1/2锛/...
绛旓細绛変簬-0.555992銆傛寮︼紙sine锛夛紝鏁板鏈锛屽湪鐩磋涓夎褰腑锛屼换鎰忎竴閿愯A鐨勫杈逛笌鏂滆竟鐨勬瘮鍙仛瑙扐鐨勬寮︼紝璁颁綔sinA锛堢敱鑻辫sine涓璇嶇畝鍐欏緱鏉ワ級锛屽嵆sinA=瑙扐鐨勫杈规瘮鏂滆竟銆
