余弦正弦转换公式 三角函数正弦和余弦的转换公式？
\u6b63\u4f59\u5f26\u8f6c\u5316\u516c\u5f0f\u8bf1\u5bfc\u516c\u5f0f\uff08\u53e3\u8bc0:\u5947\u53d8\u5076\u4e0d\u53d8,\u7b26\u53f7\u770b\u8c61\u9650.\uff09
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
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\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\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
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
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
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\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
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
(\u5176\u4e2dk\u2208Z)
\u4e24\u89d2\u548c\u4e0e\u5dee\u7684\u4e09\u89d2\u51fd\u6570\u516c\u5f0f \u4e07\u80fd\u516c\u5f0f
sin\uff08\u03b1\uff0b\u03b2\uff09\uff1dsin\u03b1cos\u03b2\uff0bcos\u03b1sin\u03b2
sin\uff08\u03b1\uff0d\u03b2\uff09\uff1dsin\u03b1cos\u03b2\uff0dcos\u03b1sin\u03b2
cos\uff08\u03b1\uff0b\u03b2\uff09\uff1dcos\u03b1cos\u03b2\uff0dsin\u03b1sin\u03b2
cos\uff08\u03b1\uff0d\u03b2\uff09\uff1dcos\u03b1cos\u03b2\uff0bsin\u03b1sin\u03b2
tan\uff08\u03b1\uff0b\u03b2\uff09\uff1d(tan\u03b1\uff0btan\u03b2)/(1\uff0dtan\u03b1 \u00b7tan\u03b2)
\u3000\u3000\u3000\u3000\u3000 tan\u03b1\uff0dtan\u03b2
tan\uff08\u03b1\uff0d\u03b2\uff09\uff1d\u2014\u2014\u2014\u2014\u2014\u2014
\u3000\u3000\u3000\u3000\u3000\u30001\uff0btan\u03b1 \u00b7tan\u03b2
\u3000\u3000\u30002tan(\u03b1/2)
sin\u03b1\uff1d\u2014\u2014\u2014\u2014\u2014\u2014
\u3000\u3000\u3000\u30001\uff0btan2(\u03b1/2)
\u3000\u3000 1\uff0dtan^2(\u03b1/2)
cos\u03b1\uff1d\u2014\u2014\u2014\u2014\u2014\u2014
\u3000\u3000\u30001\uff0btan^2(\u03b1/2)
\u3000\u3000\u30002tan(\u03b1/2)
tan\u03b1\uff1d\u2014\u2014\u2014\u2014\u2014\u2014
\u3000\u3000\u30001\uff0dtan^2(\u03b1/2)
\u534a\u89d2\u7684\u6b63\u5f26\u3001\u4f59\u5f26\u548c\u6b63\u5207\u516c\u5f0f \u4e09\u89d2\u51fd\u6570\u7684\u964d\u5e42\u516c\u5f0f
\u4e8c\u500d\u89d2\u7684\u6b63\u5f26\u3001\u4f59\u5f26\u548c\u6b63\u5207\u516c\u5f0f \u4e09\u500d\u89d2\u7684\u6b63\u5f26\u3001\u4f59\u5f26\u548c\u6b63\u5207\u516c\u5f0f
sin2\u03b1\uff1d2sin\u03b1cos\u03b1
cos2\u03b1\uff1dcos2\u03b1\uff0dsin2\u03b1\uff1d2cos2\u03b1\uff0d1\uff1d1\uff0d2sin2\u03b1
\u3000\u3000\u3000\u30002tan\u03b1
tan2\u03b1\uff1d\u2014\u2014\u2014\u2014\u2014
\u3000\u3000\u3000 1\uff0dtan^2\u03b1
sin3\u03b1\uff1d3sin\u03b1\uff0d4sin^3\u03b1
cos3\u03b1\uff1d4cos^3\u03b1\uff0d3cos\u03b1
\u3000\u3000\u30003tan\u03b1\uff0dtan^3\u03b1
tan3\u03b1\uff1d\u2014\u2014\u2014\u2014\u2014\u2014
\u3000\u3000\u3000\u30001\uff0d3tan^2\u03b1
\u4e09\u89d2\u51fd\u6570\u7684\u548c\u5dee\u5316\u79ef\u516c\u5f0f \u4e09\u89d2\u51fd\u6570\u7684\u79ef\u5316\u548c\u5dee\u516c\u5f0f
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000 \u03b1\uff0b\u03b2\u3000\u3000 \u03b1\uff0d\u03b2
sin\u03b1\uff0bsin\u03b2\uff1d2sin\u2014\u2014\u2014\u00b7cos\u2014\u2014\u2014
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000 2\u3000\u3000\u3000\u30002
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000 \u03b1\uff0b\u03b2\u3000\u3000 \u03b1\uff0d\u03b2
sin\u03b1\uff0dsin\u03b2\uff1d2cos\u2014\u2014\u2014\u00b7sin\u2014\u2014\u2014
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000 2\u3000\u3000\u3000\u30002
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u03b1\uff0b\u03b2\u3000\u3000\u3000\u03b1\uff0d\u03b2
cos\u03b1\uff0bcos\u03b2\uff1d2cos\u2014\u2014\u2014\u00b7cos\u2014\u2014\u2014
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u30002\u3000\u3000\u3000\u3000 2
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000 \u03b1\uff0b\u03b2\u3000\u3000 \u03b1\uff0d\u03b2
cos\u03b1\uff0dcos\u03b2\uff1d\uff0d2sin\u2014\u2014\u2014\u00b7sin\u2014\u2014\u2014
\u3000\u3000\u3000\u3000\u3000\u3000\u30001\u3000\u3000\u3000\u30002\u3000\u3000\u3000\u3000 2\u3000\u3000\u3000\u3000
sin\u03b1 \u00b7cos\u03b2\uff1d-[sin\uff08\u03b1\uff0b\u03b2\uff09\uff0bsin\uff08\u03b1\uff0d\u03b2\uff09]
\u3000\u3000\u3000\u3000\u3000\u30002
\u3000\u3000\u3000\u3000\u3000\u30001
cos\u03b1 \u00b7sin\u03b2\uff1d-[sin\uff08\u03b1\uff0b\u03b2\uff09\uff0dsin\uff08\u03b1\uff0d\u03b2\uff09]
\u3000\u3000\u3000\u3000\u3000\u30002
\u3000\u3000\u3000\u3000\u3000\u30001
cos\u03b1 \u00b7cos\u03b2\uff1d-[cos\uff08\u03b1\uff0b\u03b2\uff09\uff0bcos\uff08\u03b1\uff0d\u03b2\uff09]
\u3000\u3000\u3000\u3000\u3000\u30002
\u3000\u3000\u3000\u3000\u3000\u3000\u3000 1
sin\u03b1 \u00b7sin\u03b2\uff1d\u2014 -[cos\uff08\u03b1\uff0b\u03b2\uff09\uff0dcos\uff08\u03b1\uff0d\u03b2\uff09]
\u3000\u3000\u3000\u3000\u3000\u3000\u3000 2
就变成4sin20*cos20*cos40*cos80/sin20
再利用2sina*cosa=sin2a变形得
2*sin40*cos40*cos80/sin20接着变形
sin80*cos80/sin20继续
sin160/2sin20再由sina=sin（pi-a）得
sin20/2sin20=1/2
一个角的正弦值等于这个角余角的余弦值，反之亦然。所以sin10=cos80,sin50=cos40,sin70=cos20
观察发现20度40度80度依次为前者的2倍。
2sinAcosA=sin2A
从第二行通过乘以一个2sin20再除以一个sin20，反复使用该公式将20度变为40度后变为80度从而是度数统一而简化运算
绛旓細杩欐槸绠鍗曠殑鍙樺舰銆俿in a=cos 锛坧i/2-a锛 鐒跺悗涔樹互sin20鍐嶉櫎浠in20 灏卞彉鎴4sin20*cos20*cos40*cos80/sin20 鍐嶅埄鐢2sina*cosa=sin2a鍙樺舰寰 2*sin40*cos40*cos80/sin20鎺ョ潃鍙樺舰 sin80*cos80/sin20缁х画 sin160/2sin20鍐嶇敱sina=sin锛坧i-a锛夊緱 sin20/2sin20=1/2 ...
绛旓細cos鎬庝箞杞寲涓簊in锛岀浉鍏冲唴瀹瑰涓嬶細涓銆杞崲鍏紡 cos鍜宻in杞崲鍏紡鏈夛細sin锛2k蟺+伪锛=sin伪銆乧os锛2k蟺+伪锛=cos伪銆乻in锛埾+伪锛=锛峴in伪銆乧os锛埾+伪锛=锛峜os伪銆乻in锛堬紞伪锛=锛峴in伪銆乧os锛堬紞伪锛=cos伪绛夈俢os鏄浣欏鸡鍊硷紝sin鏄姝ｅ鸡鍊笺傛寮﹀兼槸鍦ㄧ洿瑙掍笁瑙掑舰涓紝瀵硅竟鐨勯暱姣斾笂鏂滆竟鐨勯暱...
绛旓細涓夎鍑芥暟sincos杞崲鍏紡濡備笅锛氫笁瑙掑嚱鏁皊incos杞崲鍏紡鏄竴缁勬暟瀛﹀叕寮忥紝鐢ㄤ簬灏姝ｅ鸡鍑芥暟锛坰in锛夊拰浣欏鸡鍑芥暟锛坈os锛夌浉浜掕浆鍖栥傝繖浜涘叕寮忓湪瑙ｅ喅鍚勭鏁板鍜岀墿鐞嗛棶棰樹腑闈炲父鏈夌敤锛屽洜姝ゅ湪鏁板鍜屽伐绋嬮鍩熷箍娉涘簲鐢ㄣ備互涓嬫槸鍏充簬杩欎簺杞崲鍏紡鐨勮缁嗕粙缁嶏紝鍏朵腑鍖呮嫭甯歌鐨剆incos杞崲鍏紡浠ュ強瀹冧滑鐨勫簲鐢ㄣ1.姝ｅ鸡鍑芥暟鍜屼綑寮﹀嚱鏁扮殑...
绛旓細鐢氳嚦鏄鏁板笺傚父瑙佺殑涓夎鍑芥暟鍖呮嫭姝ｅ鸡鍑芥暟銆浣欏鸡鍑芥暟鍜屾鍒囧嚱鏁般傚湪鑸捣瀛︺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備笉鍚岀殑涓夎鍑芥暟涔嬮棿鐨勫叧绯诲彲浠ラ氳繃鍑犱綍鐩磋鎴栬呰绠楀緱鍑猴紝绉颁负涓夎鎭掔瓑寮忋
绛旓細姝ｅ鸡瀹氱悊锛氬湪涓涓笁瑙掑舰涓紝鍚勮竟鍜屽畠鎵瀵圭殑瑙掔殑姝ｅ鸡鐨勬瘮鐩哥瓑銆傛寮﹀畾鐞鍏紡銆浣欏鸡瀹氱悊鍏紡 涓銆佹寮﹀畾鐞嗗叕寮 a/sinA=b/sinB=c/sinC=2R銆傘愭敞1銆戝叾涓淩鈥濅负涓夎褰⑩柍ABC澶栨帴鍦嗗崐寰勩備笅鍚屻傘愭敞2銆戞寮﹀畾鐞嗛傜敤浜庢墍鏈変笁瑙掑舰銆傚垵涓暟瀛︿腑锛屼笁瑙掑舰鍐呰鐨勬寮﹀肩瓑浜庘滃姣旀枩鈥濅粎閫傜敤浜庣洿瑙掍笁瑙掑舰銆備簩...
绛旓細涓夊嶈鍏紡锛歴in3伪=3sin伪-4sin^3(伪)cos3伪=4cos^3(伪)-3cos伪 鍗婅鍏紡锛歴in^2(伪/2)=(1-cos伪)/2 cos^2(伪/2)=(1+cos伪)/2 tan^2(伪/2)=(1-cos伪)/(1+cos伪)tan(伪/2)=sin伪/(1+cos伪)=(1-cos伪)/sin伪 涓囪兘鍏紡锛氬崐瑙掔殑姝ｅ鸡銆浣欏鸡鍜屾鍒囧叕寮忥紙闄嶅箓鎵╄...
绛旓細涓銆姝ｅ鸡瀹氱悊鎺ㄨ鍏紡 1銆乤=2RsinA锛沚=2RsinB锛沜=2RsinC銆2銆乤:b=sinA:sinB锛沘:c=sinA:sinC锛沚:c=sinB:sinC锛沘:b:c=sinA:sinB:sinC銆備簩銆浣欏鸡瀹氱悊鎺ㄨ鍏紡 1銆乧osA=(b^2+c^2-a^2)/2bc锛2銆乧osB=(a^2+c^2-b^2)/2ac锛3銆乧osC=(a^2+b^2-c^2)/2ab銆備笁銆佹寮﹀畾鐞嗙殑...
绛旓細sin cos tan杞崲鍏紡鏄痶an(x)=sin(x)/cos(x)銆傚悓瑙掍笁瑙掑嚱鏁扮殑鍩烘湰鍏崇郴寮忎粙缁 1銆佸掓暟鍏崇郴:tan伪 路cot伪锛1銆乻in伪 路csc伪锛1銆乧os伪 路sec伪锛1銆2銆佸叧绯伙細sin伪/cos伪锛漷an伪锛漵ec伪/csc伪銆乧os伪/sin伪锛漜ot伪锛漜sc伪/sec伪銆3銆佸钩鏂瑰叧绯伙細sin^2(伪)锛媍os^2(伪)锛1銆1锛媡an^...
绛旓細涓よ鍜岀殑姝ｅ鸡涓浣欏鸡鍏紡锛氾紙1锛塻in锛埼+尾锛=sin伪cos尾+cos伪sin尾锛涳紙2锛塩os锛埼+尾锛=cos伪cos尾-sin伪sin尾锛泂in锛埼+尾锛= cos锛90掳-伪-尾锛=cos[锛90掳-伪锛+锛-尾锛塢=cos锛90掳-伪锛塩os锛-尾锛- sin锛90掳-伪锛塻in锛-尾锛=sin伪cos尾+cos伪sin尾 鍦ㄨВ涓夎褰腑锛屾湁...
绛旓細涓夎鍑芥暟姝ｅ鸡浣欏鸡鍏紡澶у叏锛氫竴 . 涓夎鍑芥暟姝ｅ鸡浣欏鸡鍏紡 姝ｅ鸡sin=瀵硅竟姣旀枩杈广佷綑寮os=閭昏竟姣旀枩杈广佹鍒噒an=瀵硅竟姣旈偦杈广佷綑鍒嘽ot=閭昏竟姣斿杈 銆備互涓嬪浘涓轰緥锛屽湪Rt鈻矨BC锛堢洿瑙掍笁瑙掑舰锛変腑锛屼换鎰忎竴閿愯鈭燗锛屽畠鐨勫杈逛笌鏂滆竟鐨勬瘮鍙綔鈭燗鐨勬寮︼紝璁颁綔sinA锛涒垹A鐨勯偦杈逛笌鏂滆竟鐨勬瘮鍙綔鈭燗鐨勪綑寮︼紝璁颁綔cosA...
