求三角函数的一些公式
\u4e09\u89d2\u51fd\u6570\u516c\u5f0f\u5927\u5168\u4e09\u89d2\u51fd\u6570\u516c\u5f0f\u6709\u79ef\u5316\u548c\u5dee\u516c\u5f0f\u3001\u548c\u5dee\u5316\u79ef\u516c\u5f0f\u3001\u4e09\u500d\u89d2\u516c\u5f0f\u3001\u6b63\u5f26\u4e8c\u500d\u89d2\u516c\u5f0f\u3001\u4f59\u5f26\u4e8c\u500d\u89d2\u516c\u5f0f\u3001\u4f59\u5f26\u5b9a\u7406\u7b49\u30021\u79ef\u5316\u548c\u5dee\u516c\u5f0f\u3002sin\u03b1\u00b7cos\u03b2=(1/2)*[sin(\u03b1+\u03b2)+sin(\u03b1-\u03b2)]\uff1bcos\u03b1\u00b7sin\u03b2=(1/2)*[sin(\u03b1+\u03b2)-sin(\u03b1-\u03b2)];cos\u03b1\u00b7cos\u03b2=(1/2)*[cos(\u03b1+\u03b2)+cos(\u03b1-\u03b2)];sin\u03b1\u00b7sin\u03b2=-(1/2)*[cos(\u03b1+\u03b2)-cos(\u03b1-\u03b2)]2\u3001\u548c\u5dee\u5316\u79ef\u516c\u5f0f\u3002sin\u03b1+sin\u03b2=2sin[(\u03b1+\u03b2)/2]\u00b7cos[(\u03b1-\u03b2)/2];sin\u03b1-sin\u03b2=2cos[(\u03b1+\u03b2)/2]\u00b7sin[(\u03b1-\u03b2)/2]cos\u03b1+cos\u03b2=2cos[(\u03b1+\u03b2)/2]\u00b7cos[(\u03b1-\u03b2)/2];cos\u03b1-cos\u03b2=-2sin[(\u03b1+\u03b2)/2]\u00b7sin[(\u03b1-\u03b2)/2]3\u4e09\u500d\u89d2\u516c\u5f0f\u3002sin3\u03b1=3sin\u03b1-4sin^3\u03b1\uff1acos3\u03b1=4cos^3\u03b1-3cos\u03b14\u4e24\u89d2\u548c\u4e0e\u5dee\u7684\u4e09\u89d2\u51fd\u6570\u5173\u7cfbsin(\u03b1+\u03b2)=sin\u03b1cos\u03b2+cos\u03b1sin\u03b2;sin(\u03b1-\u03b2)=sin\u03b1cos\u03b2-cos\u03b1sin\u03b2;cos(\u03b1+\u03b2)=cos\u03b1cos\u03b2-sin\u03b1sin\u03b2;cos(\u03b1-\u03b2)=cos\u03b1cos\u03b2+sin\u03b1sin\u03b2;tan(\u03b1+\u03b2)=(tan\u03b1+tan\u03b2)/(1-tan\u03b1\u00b7tan\u03b2);tan(\u03b1-\u03b2)=(tan\u03b1-tan\u03b2)/(1+tan\u03b1\u00b7tan\u03b2)
\u6253\u5f00\u5de5\u4f5c\u8868\uff0c\u5728A2\u5355\u5143\u683c\u91cc\u8f93\u5165\u8981\u8ba1\u7b97\u7684\u89d2\u5ea6\u503c\uff0c\u5728B2,C2,D2\u5355\u5143\u683c\u4e2d\u5206\u522b\u8f93\u5165\u9700\u8981\u8ba1\u7b97\u7684\u4e09\u89d2\u51fd\u6570\uff1b
\u6b63\u5f26\u51fd\u6570\u8ba1\u7b97\u516c\u5f0f\uff0c\u5728B2\u5355\u5143\u683c\u4e2d\u8f93\u5165\uff1a=SIN(A1*PI()/180)\uff1b
\u4f59\u5f26\u51fd\u6570\u8ba1\u7b97\u516c\u5f0f\uff0c\u5728C2\u5355\u5143\u683c\u4e2d\u8f93\u5165\uff1a=COS(A1*PI()/180)\uff1b
\u6b63\u5207\u51fd\u6570\u8ba1\u7b97\u516c\u5f0f\uff0c\u5728D2\u5355\u5143\u683c\u4e2d\u8f93\u5165\uff1a=TAN(A1*PI()/180)\uff1b
\u9009\u5b9aB2,C2,D2\u4e09\u4e2a\u5355\u5143\u683c\uff0c\u7528\u62d6\u62c9\u7684\u65b9\u5f0f\u5c06\u4e0a\u9762\u7684\u516c\u5f0f\u590d\u5236\u5230\u4e0b\u9762\u51e0\u4e2a\u5355\u5143\u683c\uff1b\u5728A2.....6\u5355\u5143\u683c\u4e2d\u8f93\u5165\u4e0d\u540c\u7684\u89d2\u5ea6\u503c\uff0c\u5728\u5bf9\u5e94\u7684\u8ba1\u7b97\u51fd\u6570\u5355\u5143\u683c\u4e2d\u5c31\u663e\u793a\u51fa\u76f8\u5e94\u7684\u8ba1\u7b97\u7ed3\u679c\u3002
cosx/sinx=cotx
(sinx)^2+(cosx)^2=1
sinx=1/(cscx)
cosx=1/(secx)
两角和与差公式:
sin(x+y)=sinxcosy+cosxsiny,sin(x-y)=sinxcosy-cosxsiny
cos(x+y)=cosxcosy-sinxsiny,cos(x-y)=cosxcosy+sinxsiny
tan(x+y)=[tanx+tany]/[1-tanxtany],tan(x-y)=[tanx-tany]/[1+tanxtany]
二倍角公式:
sin2x=2sinxcosx;
cos2x=(cosx)^2-(sinx)^2=2(cosx)^2-1=1-2(sinx)^2
tan2x=2tanx/[1-(tanx)^2]
半角公式:
sinx/2=±√[(1-cosx)/2]
cosx/2=±√[(1+cosx)/2]
tanx/2=±√[(1-cosx)/(1+cosx)]=sinx/(1+cosx)=(1-cosx)/sinx
积化和差:
sinxsiny=-[cos(x+y)-cos(x-y)]/2
cosxcosy=[cos(x+y)+cos(x-y)]/2
sinxcosy=[sin(x+y)+sin(x-y)]/2
cosxsiny=[sin(x+y)-sin(x-y)]/2
和差化积:
sinx+siny=2[sin(x+y)/2][cos(x-y)/2]
sinx-siny=2[cos(x+y)/2][sin(x-y)/2]
cosx+cosy=2[cos(x+y)/2][cos(x-y)/2]
cosx-cosy=-2[sin(x+y)/2][sin(x-y)/2]
绛旓細01 涓夎鍑芥暟鍏紡鍖呮嫭鍜屽樊瑙掑叕寮忋佸拰宸寲绉叕寮忋佺Н鍖栧拰宸叕寮忋佸嶈鍏紡绛夈備笁瑙掑嚱鏁板叕寮忔槸鏁板涓睘浜庡垵绛夊嚱鏁颁腑鐨勮秴瓒鍑芥暟鐨涓绫诲嚱鏁板叕寮忋傚畠浠殑鏈川鏄换鎰忚鐨勯泦鍚堜笌涓涓瘮鍊肩殑闆嗗悎鐨勫彉閲忎箣闂寸殑鏄犲皠锛岄氬父鐨勪笁瑙掑嚱鏁版槸鍦ㄥ钩闈㈢洿瑙掑潗鏍囩郴涓畾涔夌殑銆1銆佸悓瑙掍笁瑙掑嚱鏁板熀鏈叧绯伙細鍊掓暟鍏崇郴锛歵anα&mid...
绛旓細01銆涓夎鍑芥暟鍏紡鍖呮嫭鍜屽樊瑙掑叕寮忋佸拰宸寲绉叕寮忋佺Н鍖栧拰宸叕寮忋佸嶈鍏紡绛夈備笁瑙掑嚱鏁板叕寮忔槸鏁板涓睘浜庡垵绛夊嚱鏁颁腑鐨勮秴瓒鍑芥暟鐨涓绫诲嚱鏁板叕寮忋傚畠浠殑鏈川鏄换鎰忚鐨勯泦鍚堜笌涓涓瘮鍊肩殑闆嗗悎鐨勫彉閲忎箣闂寸殑鏄犲皠锛岄氬父鐨勪笁瑙掑嚱鏁版槸鍦ㄥ钩闈㈢洿瑙掑潗鏍囩郴涓畾涔夌殑銆1銆佸悓瑙掍笁瑙掑嚱鏁板熀鏈叧绯伙細鍊掓暟鍏崇郴锛歵ancot=1 sincsc...
绛旓細cos胃-cos蠁=-2sin(胃/2+蠁/2)sin(胃/2-蠁/2)绉寲鍜屽樊 sin伪sin尾=-1/2[cos(伪+尾)-cos(伪-尾)]cos伪cos尾= 1/2[cos(伪+尾)+cos(伪-尾)]sin伪cos尾= 1/2[sin(伪+尾)+sin(伪-尾)]cos伪sin尾= 1/2[sin(伪+尾)-sin(伪-尾)]涓夊嶈鍏紡锛歴in3伪=3sin伪-4sin^3...
绛旓細1銆佸父鐢ㄧ殑涓夎鍑芥暟鍏紡 sin =瀵硅竟 / 鏂滆竟 cos =閭昏竟 / 鏂滆竟 tan =瀵硅竟 / 閭昏竟 cot =閭昏竟 / 瀵硅竟 2銆佸嶈鍏紡 Sin2A=2SinACosA Cos2A=CosA^2-SinA^2=1-2SinA^2=2CosA^2-1 tan2A=(2tanA)/(1-tanA^2) (娉細SinA^2 鏄痵inA鐨勫钩鏂 sin2(A) )3銆佷笁鍊嶈鍏紡 sin3=4sinsin(/...
绛旓細9銆佸叾瀹鍏紡 a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c) [鍏朵腑锛宼an(c)=b/a]a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c) [鍏朵腑锛宼an(c)=a/b]1+sin(a)=(sin(a/2)+cos(a/2))^2 1-sin(a)=(sin(a/2)-cos(a/2))^2 10銆佸叾浠栭潪閲嶇偣涓夎鍑芥暟 csc(a)=1/...
绛旓細sinx/cosx=tanx cosx/sinx=cotx (sinx)^2+(cosx)^2=1 sinx=1/(cscx)cosx=1/(secx)涓よ鍜屼笌宸鍏紡:sin(x+y)=sinxcosy+cosxsiny,sin(x-y)=sinxcosy-cosxsiny cos(x+y)=cosxcosy-sinxsiny,cos(x-y)=cosxcosy+sinxsiny tan(x+y)=[tanx+tany]/[1-tanxtany],tan(x-y)=[tanx-tany...
绛旓細sinA锛濆杈/鏂滆竟锛宑osA锛濋偦杈/鏂滆竟锛泂in60搴︼紳1/2锛宻in45搴︼紳鏍瑰彿2/2锛沜os60搴︼紳鏍瑰彿3/2锛宑os蟺/4锛濇牴鍙2/2銆涓夎鍑芥暟鍦ㄧ爺绌朵笁瑙掑舰鍜屽渾绛夊嚑浣曞舰鐘剁殑鎬ц川鏃舵湁閲嶈浣滅敤锛屼篃鏄爺绌跺懆鏈熸х幇璞＄殑鍩虹鏁板宸ュ叿銆傚湪鏁板鍒嗘瀽涓紝涓夎鍑芥暟涔熻瀹氫箟涓烘棤绌风骇鏁版垨鐗瑰畾寰垎鏂圭▼鐨勮В锛屽厑璁稿畠浠殑鍙栧兼墿灞曞埌浠绘剰...
绛旓細涓夎鍑芥暟12涓熀鏈鍏紡锛歴in胃=y/r銆乧os胃=x/r銆乼an胃=y/x銆乧ot胃=x/y銆乻ec胃=r/x銆乧sc胃=r/y銆乻ina=tana*cosa銆乧osa=cota*sina銆乼ana=sina*seca銆乧ota=cosa*csca銆乻eca=tana*csca銆乧sca=seca*cota銆備笁瑙掑嚱鏁版槸鏁板涓睘浜庡垵绛夊嚱鏁颁腑鐨勮秴瓒鍑芥暟鐨鍑芥暟銆傚畠浠殑鏈川鏄换浣曡鐨勯泦鍚堜笌涓涓瘮鍊...
绛旓細姝ｅ鸡鍑芥暟sin胃锛漼/r銆備綑寮﹀嚱鏁癱os胃锛漻/r銆傛鍒囧嚱鏁皌an胃锛漼/x銆備綑鍒囧嚱鏁癱ot胃锛漻/y銆傛鍓插嚱鏁皊ec胃锛漴/x銆備綑鍓插嚱鏁癱sc胃锛漴/y銆備笁瑙掑嚱鏁鍏紡缁ф硶锛1銆佲滃鍙樺伓涓嶅彉锛岀鍙风湅璞￠檺鈥濓細鈥滃銆佸伓鈥濇寚鐨勬槸蟺锛2鐨勫嶆暟鐨勫鍋讹紝鈥滃彉涓庝笉鍙樷濇寚鐨勬槸涓夎鍑芥暟鐨鍚嶇О鐨勫彉鍖栵細鈥滃彉鈥濇槸鎸囨寮﹀彉浣欏鸡锛...
绛旓細涓囪兘鍏紡: sin伪=2tan(伪梅2)梅[1+tan²(伪梅2)]cos伪=[1-tan²(伪梅2)]梅[1+tan²(伪梅2)]tan伪=2tan(伪梅2)梅[1-tan²(伪梅2)]骞抽潰涓夎褰㈠唴鐨勫叕寮:姝ｅ鸡瀹氱悊 :a梅sinA=b梅sinB=c梅sinC=2R (R涓哄鎺ュ渾鍗婂緞=abc/4S)浣欏鸡瀹氱悊:a²=b²+c&s...
