三角函数sin、cos、tan的π/几都可以化成分数·比如sinπ/3=根号3/2那其他的π/6、π/12呢 cos（－5π／6）是多少？sin （－5π／6）呢？多谢
sin cos tan\u4e4b\u95f4\u7684\u5173\u7cfb\u8fd8\u6709\u5404\u79cd\u516c\u5f0f\uff0c\u9ebb\u70e6\u5217\u4e00\u4e0b\u51fa\u6765\uff0c\u5168\u9762\u70b9\uff0c\u5230\u5927\u5b66\u5168\u5fd8\u4e86\u516c\u5f0f\u4e00\uff1a
\u8bbe\u03b1\u4e3a\u4efb\u610f\u89d2\uff0c\u7ec8\u8fb9\u76f8\u540c\u7684\u89d2\u7684\u540c\u4e00\u4e09\u89d2\u51fd\u6570\u7684\u503c\u76f8\u7b49\uff1a
sin\uff082k\u03c0\uff0b\u03b1\uff09\uff1dsin\u03b1
cos\uff082k\u03c0\uff0b\u03b1\uff09\uff1dcos\u03b1
tan\uff082k\u03c0\uff0b\u03b1\uff09\uff1dtan\u03b1
cot\uff082k\u03c0\uff0b\u03b1\uff09\uff1dcot\u03b1
\u516c\u5f0f\u4e8c\uff1a
\u8bbe\u03b1\u4e3a\u4efb\u610f\u89d2\uff0c\u03c0+\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0\uff0b\u03b1\uff09\uff1d\uff0dsin\u03b1
cos\uff08\u03c0\uff0b\u03b1\uff09\uff1d\uff0dcos\u03b1
tan\uff08\u03c0\uff0b\u03b1\uff09\uff1dtan\u03b1
cot\uff08\u03c0\uff0b\u03b1\uff09\uff1dcot\u03b1
\u516c\u5f0f\u4e09\uff1a
\u4efb\u610f\u89d2\u03b1\u4e0e -\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\uff0d\u03b1\uff09\uff1d\uff0dsin\u03b1
cos\uff08\uff0d\u03b1\uff09\uff1dcos\u03b1
tan\uff08\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1
cot\uff08\uff0d\u03b1\uff09\uff1d\uff0dcot\u03b1
\u516c\u5f0f\u56db\uff1a
\u5229\u7528\u516c\u5f0f\u4e8c\u548c\u516c\u5f0f\u4e09\u53ef\u4ee5\u5f97\u5230\u03c0-\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0\uff0d\u03b1\uff09\uff1dsin\u03b1
cos\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dcos\u03b1
tan\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1
cot\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dcot\u03b1
\u516c\u5f0f\u4e94\uff1a
\u5229\u7528\u516c\u5f0f\u4e00\u548c\u516c\u5f0f\u4e09\u53ef\u4ee5\u5f97\u52302\u03c0-\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff082\u03c0\uff0d\u03b1\uff09\uff1d\uff0dsin\u03b1
cos\uff082\u03c0\uff0d\u03b1\uff09\uff1dcos\u03b1
tan\uff082\u03c0\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1
cot\uff082\u03c0\uff0d\u03b1\uff09\uff1d\uff0dcot\u03b1
\u516c\u5f0f\u516d\uff1a
\u03c0/2\u00b1\u03b1\u53ca3\u03c0/2\u00b1\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0/2\uff0b\u03b1\uff09\uff1dcos\u03b1
cos\uff08\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dsin\u03b1
tan\uff08\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dcot\u03b1
cot\uff08\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dtan\u03b1
sin\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dcos\u03b1
cos\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dsin\u03b1
tan\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dcot\u03b1
cot\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dtan\u03b1
sin\uff083\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dcos\u03b1
cos\uff083\u03c0/2\uff0b\u03b1\uff09\uff1dsin\u03b1
tan\uff083\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dcot\u03b1
cot\uff083\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dtan\u03b1
sin\uff083\u03c0/2\uff0d\u03b1\uff09\uff1d\uff0dcos\u03b1
cos\uff083\u03c0/2\uff0d\u03b1\uff09\uff1d\uff0dsin\u03b1
tan\uff083\u03c0/2\uff0d\u03b1\uff09\uff1dcot\u03b1
cot\uff083\u03c0/2\uff0d\u03b1\uff09\uff1dtan\u03b1
(\u4ee5\u4e0ak\u2208Z)
sin0=0
sin\u03c0/6=0.5
sin\u03c0/4=\u4e8c\u5206\u4e4b\u6839\u53f72
sin\u03c0/3=\u4e8c\u5206\u4e4b\u6839\u53f73
sin\u03c0/2=1
cos0=1
cos\u03c0/6=\u4e8c\u5206\u4e4b\u6839\u53f73
cos\u03c0/4=\u4e8c\u5206\u4e4b\u6839\u53f72
cos\u03c0/3=0.5
cos\u03c0/2=0
tan0=0
tan\u03c0/6=\u4e09\u5206\u4e4b\u6839\u53f73
tan\u03c0/4=1
tan\u03c0/3=\u6839\u53f73
tan\u03c0/2\u65e0\u5b9e\u4e49
cot0 \u65e0\u5b9e\u4e49
cot\u03c0/6=\u6839\u53f73
cot\u03c0/4=1
cot\u03c0/3=\u4e09\u5206\u4e4b\u6839\u53f73
cotv/2=0
O(\u2229_\u2229)O~
\u518d\u7ed9\u4f60\u53d1\u4e00\u4e9b\u8f85\u52a9\u516c\u5f0f
\u4e00\uff09\u4e24\u89d2\u548c\u5dee\u516c\u5f0f \uff08\u5199\u7684\u90fd\u8981\u8bb0\uff09
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
\u4e8c\uff09\u7528\u4ee5\u4e0a\u516c\u5f0f\u53ef\u63a8\u51fa\u4e0b\u5217\u4e8c\u500d\u89d2\u516c\u5f0f
tan2A=2tanA/[1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2
\uff08\u4e0a\u9762\u8fd9\u4e2a\u4f59\u5f26\u7684\u5f88\u91cd\u8981\uff09
sin2A=2sinA*cosA
\u4e09\uff09\u534a\u89d2\u7684\u53ea\u9700\u8bb0\u4f4f\u8fd9\u4e2a\uff1a
tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA)
\u56db\uff09\u7528\u4e8c\u500d\u89d2\u4e2d\u7684\u4f59\u5f26\u53ef\u63a8\u51fa\u964d\u5e42\u516c\u5f0f
(sinA)^2=(1-cos2A)/2
(cosA)^2=(1+cos2A)/2
\u4e94\uff09\u7528\u4ee5\u4e0a\u964d\u5e42\u516c\u5f0f\u53ef\u63a8\u51fa\u4ee5\u4e0b\u5e38\u7528\u7684\u5316\u7b80\u516c\u5f0f
1-cosA=sin^(A/2)*2
1-sinA=cos^(A/2)*2
\u4e00\uff09\u4e24\u89d2\u548c\u5dee\u516c\u5f0f \uff08\u5199\u7684\u90fd\u8981\u8bb0\uff09
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
\u4e8c\uff09\u7528\u4ee5\u4e0a\u516c\u5f0f\u53ef\u63a8\u51fa\u4e0b\u5217\u4e8c\u500d\u89d2\u516c\u5f0f
tan2A=2tanA/[1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2
\uff08\u4e0a\u9762\u8fd9\u4e2a\u4f59\u5f26\u7684\u5f88\u91cd\u8981\uff09
sin2A=2sinA*cosA
\u4e09\uff09\u534a\u89d2\u7684\u53ea\u9700\u8bb0\u4f4f\u8fd9\u4e2a\uff1a
tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA)
\u56db\uff09\u7528\u4e8c\u500d\u89d2\u4e2d\u7684\u4f59\u5f26\u53ef\u63a8\u51fa\u964d\u5e42\u516c\u5f0f
(sinA)^2=(1-cos2A)/2
(cosA)^2=(1+cos2A)/2
\u4e94\uff09\u7528\u4ee5\u4e0a\u964d\u5e42\u516c\u5f0f\u53ef\u63a8\u51fa\u4ee5\u4e0b\u5e38\u7528\u7684\u5316\u7b80\u516c\u5f0f
1-cosA=sin^(A/2)*2
1-sinA=cos^(A/2)*2
\u540c\u89d2\u4e09\u89d2\u51fd\u6570\u57fa\u672c\u5173\u7cfb
\u2488\u540c\u89d2\u4e09\u89d2\u51fd\u6570\u7684\u57fa\u672c\u5173\u7cfb\u5f0f
\u5012\u6570\u5173\u7cfb:
tan\u03b1 \u00b7cot\u03b1\uff1d1
sin\u03b1 \u00b7csc\u03b1\uff1d1
cos\u03b1 \u00b7sec\u03b1\uff1d1
\u5546\u7684\u5173\u7cfb\uff1a
sin\u03b1/cos\u03b1\uff1dtan\u03b1\uff1dsec\u03b1/csc\u03b1
cos\u03b1/sin\u03b1\uff1dcot\u03b1\uff1dcsc\u03b1/sec\u03b1
\u5e73\u65b9\u5173\u7cfb\uff1a
sin^2(\u03b1)\uff0bcos^2(\u03b1)\uff1d1
1\uff0btan^2(\u03b1)\uff1dsec^2(\u03b1)
1\uff0bcot^2(\u03b1)\uff1dcsc^2(\u03b1)
\u5e0c\u671b\u80fd\u5e2e\u5230\u4f60\uff0c\u8bf7\u91c7\u7eb3\u6b63\u786e\u7b54\u6848\uff0c\u70b9\u51fb\u3010\u91c7\u7eb3\u7b54\u6848\u3011\uff0c\u8c22\u8c22 ^_^
cos(-5\u03c0/6)\u662f-\u221a3/2\uff0csin(-5\u03c0/6)\u662f-1/2\u3002
\u89e3\uff1acos(-5\u03c0/6)=cos(5\u03c0/6)
=-cos(\u03c0-5\u03c0/6)
=-cos(\u03c0/6)=-\u221a3/2
sin(-5\u03c0/6)=-sin(5\u03c0/6)
=-sin(\u03c0-5\u03c0/6)
=-sin(\u03c0/6)=-1/2
\u5373cos(-5\u03c0/6)\u7684\u503c\u4e3a-\u221a3/2\uff0csin(-5\u03c0/6)\u7684\u503c\u4e3a-1/2\u3002
\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u5e38\u89c1\u7684\u4e09\u89d2\u51fd\u6570\u5305\u62ec\u6b63\u5f26\u51fd\u6570\uff08sin\uff09\u3001\u4f59\u5f26\u51fd\u6570\uff08cos\uff09\u3001\u6b63\u5207\u51fd\u6570\uff08tan\uff09\u53ca\u4f59\u5207\u51fd\u6570\uff08cot\uff09\u3002
2\u3001\u5e38\u89c1\u4e09\u89d2\u51fd\u6570\u4e4b\u95f4\u7684\u5173\u7cfb
sin(-x)=-sinx\u3001cos(-x)=cosx\u3001cosx=-cos(\u03c0-x)\u3001sinx=sin(\u03c0-x)\u3001sinx=cos\uff08\u03c0/2-x\uff09\u3001cosx=cos\uff08\u03c0/2-x\uff09\u3002
3\u3001\u7279\u6b8a\u89d2\u7684\u4e09\u89d2\u51fd\u6570\u503c
sin\u03c0/6=1/2\u3001cos\u03c0/6=\u221a3/2\u3001tan\u03c0/6=\u221a3/3\u3001cot\u03c0/6=\u221a3
sin\u03c0/4=\u221a2/2\u3001cos\u03c0/4=\u221a2/2\u3001tan\u03c0/4=1\u3001cot\u03c0/4=1\u3001
sin\u03c0/3=\u221a3/2\u3001cos\u03c0/3=1/2\u3001tan\u03c0/3=\u221a3\u3001cot\u03c0/3=\u221a3/3
sin\u03c0/2=1\u3001cos\u03c0/2=0\u3001tan\u03c0/2\u4e0d\u5b58\u5728\u3001cot\u03c0/2=0
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u4e09\u89d2\u51fd\u6570
sin0=0,
sin15=（√6-√2)/4 ,
sin30=1/2,
sin45=√2/2,
sin60=√3/2,
sin75=(√6+√2)/4 ,
sin90=1,
sin105=(√6+√2)/4
sin120=√3/2
sin135=√2/2
sin150=1/2
sin165=（√6-√2)/4
sin180=0
sin270=-1
sin360=0
cos0=1
tan0=0
cos15=（√6+√2）/4
tan15=sin15/cos15=2-√3
cos30=√3/2
tan30=√3/3
cos45=sin45=√2/2
tan45=1
cos60=1/2
tan60=√3
cos75=sin15
tan75=sin75/cos75 ＝2＋√3
cos90=sin0
tan90无意义
cos105=-sin15
tan105=-cot15
cos120=-sin30
tan120=-tan60
cos135=-cos45
tan135=-tan45
cos150=-cos30
tan150=-tan30
cos165=-cos15
tan165=-tan15
cos180=-cos0
tan180=tan0
cos195=-cos15
tan195=tan15
cos360=cos0
tan360=tan0
0，π/6,π/3,π/4,π/2,π/2,2/3π,5/6π,3/4π,π,7/6π,4/3π,5/4π,3/2π,11/6π,5/3π,7/4π,2π.这些都可以,它们的三角函数值都是要求我们记忆的.高中课本上都有
绛旓細鐢变簬涓夎鍑芥暟鐨勫懆鏈熸э紝瀹冨苟涓嶅叿鏈夊崟鍊煎嚱鏁版剰涔変笂鐨勫弽鍑芥暟銆備笁瑙掑嚱鏁板湪澶嶆暟涓湁杈冧负閲嶈鐨勫簲鐢ㄣ傚湪鐗╃悊瀛︿腑锛屼笁瑙掑嚱鏁颁篃鏄父鐢ㄧ殑宸ュ叿銆傚熀鏈垵绛夊唴瀹 瀹冩湁鍏鍩烘湰鍑芥暟(鍒濈瓑鍩烘湰琛ㄧず)锛氬嚱鏁板悕 姝ｅ鸡 浣欏鸡 姝ｅ垏 浣欏垏 姝ｅ壊 浣欏壊 姝ｅ鸡鍑芥暟 sin胃=y/r 浣欏鸡鍑芥暟 cos胃=x/r 姝ｅ垏鍑芥暟 tan胃=y/x 浣欏垏鍑芥暟 ...
绛旓細SIN锛氣垹A鐨勫杈规瘮鏂滆竟=a/c COS锛氣垹A鐨勯偦杈规瘮鏂滆竟=b/c TAN锛氣垹A鐨勫杈规瘮閭昏竟=a/b COT锛氣垹A鐨勯偦杈规瘮瀵硅竟=b/a
绛旓細cot 伪=鈭犖辩殑閭昏竟 / 鈭犖辩殑瀵硅竟銆傝儗璇绐嶏細濂囧彉鍋朵笉鍙橈紝绗﹀彿鐪嬭薄闄愶紟鍗冲舰濡傦紙2k+1锛90掳卤伪锛屽垯鍑芥暟鍚嶇О鍙樹负浣欏悕鍑芥暟锛屾寮﹀彉浣欏鸡锛屼綑寮﹀彉姝ｅ鸡锛屾鍒囧彉浣欏垏锛屼綑鍒囧彉姝ｅ垏锛屽舰濡2k脳90掳卤伪锛屽垯鍑芥暟鍚嶇О涓嶅彉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^...
绛旓細1銆佹寮鍑芥暟y=sinx 澧炲尯闂达細[-蟺/2+2k蟺锛屜/2+2k蟺]锛坘鈭圸锛夊噺鍖洪棿锛歔蟺/2+2k蟺锛3蟺/2+2k蟺]锛坘鈭圸锛2銆佷綑寮﹀嚱鏁皔=cosx 澧炲尯闂达細[-蟺+2k蟺锛2k蟺]锛坘鈭圸锛夊噺鍖洪棿锛歔2k蟺锛屜+2k蟺]锛坘鈭圸锛3銆佹鍒囧嚱鏁皔=tanx 澧炲尯闂达細[-蟺/2+k蟺锛屜/2+k蟺]锛坘鈭圸锛墆=tanx鏃犲噺...
绛旓細1銆sin30 掳 = 1/2 2銆乻in45 掳 =鏍瑰彿2/2 3銆乻in60 掳 = 鏍瑰彿3/2 浜屻cos搴︽暟鍏紡 1銆乧os30 掳 =鏍瑰彿3/2 2銆乧os45 掳 =鏍瑰彿2/2 3銆乧os60 掳 =1/2 涓夈tan搴︽暟鍏紡 1銆乼an30 掳 =鏍瑰彿3/3 2銆乼an45 掳 =1 3銆乼an60 掳 =鏍瑰彿3 cos sin tan搴︽暟鍏紡琛ㄥ涓嬶細涓夎鍑芥暟 ...
绛旓細锛3锛塩ot^2(伪)+1=csc^2(伪)2銆佺Н鐨勫叧绯伙細锛1锛sin伪=tan伪*cos伪 锛2锛塩os伪=cot伪*sin伪 锛3锛塼an伪=sin伪*sec伪 锛4锛塩ot伪=cos伪*csc伪 锛5锛塻ec伪=tan伪*csc伪 锛6锛塩sc伪=sec伪*cot伪 3銆佸掓暟鍏崇郴锛氾紙1锛塼an伪路cot伪=1 锛2锛塻in伪路csc伪=1 锛3锛塩os伪路sec伪=...
绛旓細浣欏垏:cot(cotangent鐨勭缉鍐,璇讳綔:'kou tan zhen te),瑙捨辩殑姝ｅ垏涓庝綑鍒囦簰涓哄掓暟銆備笅鍥捐〃绀轰簡瑙捨辩殑涓夎鍑芥暟鐨勫畾涔夈備笅闈㈠垪鍑轰簡涓浜涚壒娈婅鐨勪笁瑙掑嚱鏁板笺備笁瑙掑嚱鏁扮殑璇卞鍏紡:sin(-伪)=-sin(伪)cos(-伪)=cos(伪)sin(蟺-伪)=sin(伪)cos(蟺-伪)=-cos(伪)sin(蟺+伪)=-sin(伪)cos(蟺+伪)=...
绛旓細姝ｅ鸡sin=瀵硅竟姣旀枩杈广備綑寮os=閭昏竟姣旀枩杈广傛鍒嘾utan=瀵硅竟姣旈偦zhi杈广tan鏄杈规瘮閭昏竟锛宻in瀵硅竟姣旀枩杈锛宑os鏄偦杈规瘮鏂滆竟銆傜洿瑙涓夎褰腑锛寊hi姝ｅ鸡绛変簬瀵硅竟姣旀枩杈逛綑寮︾瓑浜庨偦杈规瘮鏂滆竟锛屾鍒囩瓑浜庡杈规瘮閭昏竟銆
绛旓細cos鏄偦杈规瘮鏂滆竟锛sin鏄杈规瘮鏂滆竟锛宼an鏄杈规瘮閭昏竟銆傚湪鐩磋涓夎褰㈠綋涓紝姝ｅ鸡鏄瓑浜庡杈规瘮鏂滆竟锛屼綑寮︾瓑浜庨偦杈规瘮鏂滆竟锛屾鍒囩瓑浜庡杈规瘮閭昏竟銆涓夎鍑芥暟鏄垵绛夊嚱鏁颁箣涓锛岃浠ヨ瑙掍负鍙橀噺锛岃瑙掔浉鍖归厤浠绘剰瑙掔粓杈逛笌鍗曚綅鍦嗕氦鐐瑰潗鏍囨垨鑰呭叾姣旂巼涓鸿В閲婂彉閲忕殑鍑芥暟鍏紡锛岃繕鍙互绛夐鐨勫湴鐢ㄤ笌鍗曚綅鍦嗙浉鍏崇殑鍚勭鍚勬牱绾挎鐨...
绛旓細sin锛氬杈规瘮鏂滆竟 cos锛氫复杈规瘮鏂滆竟 tan锛氬杈规瘮涓磋竟
