Tan的公式
sin cos tan\u6240\u6709\u516c\u5f0f\u4e24\u89d2\u548c\u516c\u5f0f
\u3000\u3000sin(A+B) = sinAcosB+cosAsinB
\u3000\u3000sin(A-B) = sinAcosB-cosAsinB �
\u3000\u3000cos(A+B) = cosAcosB-sinAsinB
\u3000\u3000cos(A-B) = cosAcosB+sinAsinB
\u3000\u3000tan(A+B) = (tanA+tanB)/(1-tanAtanB)
\u3000\u3000tan(A-B) = (tanA-tanB)/(1+tanAtanB)
\u3000\u3000cot(A+B) = (cotAcotB-1)/(cotB+cotA) �
\u3000\u3000cot(A-B) = (cotAcotB+1)/(cotB-cotA)
[\u7f16\u8f91\u672c\u6bb5]\u500d\u89d2\u516c\u5f0f
\u3000\u3000tan2A = 2tanA/(1-tan^2 A)
\u3000\u3000Sin2A=2SinA�6�1CosA
\u3000\u3000Cos2A = Cos^2 A--Sin^2 A
\u3000\u3000=2Cos^2 A\u20141
\u3000\u3000=1\u20142sin^2 A
[\u7f16\u8f91\u672c\u6bb5]\u4e09\u500d\u89d2\u516c\u5f0f
\u3000\u3000sin3A = 3sinA-4(sinA)^3;
\u3000\u3000cos3A = 4(cosA)^3 -3cosA
\u3000\u3000tan3a = tan a \u00b7 tan(\u03c0/3+a)\u00b7 tan(\u03c0/3-a)
[\u7f16\u8f91\u672c\u6bb5]\u534a\u89d2\u516c\u5f0f
\u3000\u3000sin(A/2) = \u221a{(1--cosA)/2}
\u3000\u3000cos(A/2) = \u221a{(1+cosA)/2}
\u3000\u3000tan(A/2) = \u221a{(1--cosA)/(1+cosA)}
\u3000\u3000cot(A/2) = \u221a{(1+cosA)/(1-cosA)} �
\u3000\u3000tan(A/2) = (1--cosA)/sinA=sinA/(1+cosA)
[\u7f16\u8f91\u672c\u6bb5]\u548c\u5dee\u5316\u79ef
\u3000\u3000sin(a)+sin(b) = 2sin[(a+b)/2]cos[(a-b)/2]
\u3000\u3000sin(a)-sin(b) = 2cos[(a+b)/2]sin[(a-b)/2]
\u3000\u3000cos(a)+cos(b) = 2cos[(a+b)/2]cos[(a-b)/2]
\u3000\u3000cos(a)-cos(b) = -2sin[(a+b)/2]sin[(a-b)/2]
\u3000\u3000tanA+tanB=sin(A+B)/cosAcosB
[\u7f16\u8f91\u672c\u6bb5]\u79ef\u5316\u548c\u5dee
\u3000\u3000sin(a)sin(b) = -1/2*[cos(a+b)-cos(a-b)]
\u3000\u3000cos(a)cos(b) = 1/2*[cos(a+b)+cos(a-b)]
\u3000\u3000sin(a)cos(b) = 1/2*[sin(a+b)+sin(a-b)]
\u3000\u3000cos(a)sin(b) = 1/2*[sin(a+b)-sin(a-b)]
[\u7f16\u8f91\u672c\u6bb5]\u8bf1\u5bfc\u516c\u5f0f
\u3000\u3000sin(-a) = -sin(a)
\u3000\u3000cos(-a) = cos(a)
\u3000\u3000sin(\u03c0/2-a) = cos(a)
\u3000\u3000cos(\u03c0/2-a) = sin(a)
\u3000\u3000sin(\u03c0/2+a) = cos(a)
\u3000\u3000cos(\u03c0/2+a) = -sin(a)
\u3000\u3000sin(\u03c0-a) = sin(a)
\u3000\u3000cos(\u03c0-a) = -cos(a)
\u3000\u3000sin(\u03c0+a) = -sin(a)
\u3000\u3000cos(\u03c0+a) = -cos(a)
\u3000\u3000tgA=tanA = sinA/cosA
[\u7f16\u8f91\u672c\u6bb5]\u4e07\u80fd\u516c\u5f0f
\u3000\u3000sin(a) = [2tan(a/2)] / {1+[tan(a/2)]^2}
\u3000\u3000cos(a) = {1-[tan(a/2)]^2} / {1+[tan(a/2)]^2}
\u3000\u3000tan(a) = [2tan(a/2)]/{1-[tan(a/2)]^2}
[\u7f16\u8f91\u672c\u6bb5]\u5176\u5b83\u516c\u5f0f
\u3000\u3000a\u00b7sin(a)+b\u00b7cos(a) = [\u221a(a^2+b^2)]*sin(a+c) [\u5176\u4e2d\uff0ctan(c)=b/a]
\u3000\u3000a\u00b7sin(a)-b\u00b7cos(a) = [\u221a(a^2+b^2)]*cos(a-c) [\u5176\u4e2d\uff0ctan(c)=a/b]
\u3000\u30001+sin(a) = [sin(a/2)+cos(a/2)]^2;
\u3000\u30001-sin(a) = [sin(a/2)-cos(a/2)]^2;;
[\u7f16\u8f91\u672c\u6bb5]\u5176\u4ed6\u975e\u91cd\u70b9\u4e09\u89d2\u51fd\u6570
\u3000\u3000csc(a) = 1/sin(a)
\u3000\u3000sec(a) = 1/cos(a)
[\u7f16\u8f91\u672c\u6bb5]\u53cc\u66f2\u51fd\u6570
\u3000\u3000sinh(a) = [e^a-e^(-a)]/2
\u3000\u3000cosh(a) = [e^a+e^(-a)]/2
\u3000\u3000tg h(a) = sin h(a)/cos h(a)
\u3000\u3000\u516c\u5f0f\u4e00\uff1a
\u3000\u3000\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
\u3000\u3000sin\uff082k\u03c0\uff0b\u03b1\uff09= sin\u03b1
\u3000\u3000cos\uff082k\u03c0\uff0b\u03b1\uff09= cos\u03b1
\u3000\u3000tan\uff082k\u03c0\uff0b\u03b1\uff09= tan\u03b1
\u3000\u3000cot\uff082k\u03c0\uff0b\u03b1\uff09= cot\u03b1
\u3000\u3000\u516c\u5f0f\u4e8c\uff1a
\u3000\u3000\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
\u3000\u3000sin\uff08\u03c0\uff0b\u03b1\uff09= -sin\u03b1
\u3000\u3000cos\uff08\u03c0\uff0b\u03b1\uff09= -cos\u03b1
\u3000\u3000tan\uff08\u03c0\uff0b\u03b1\uff09= tan\u03b1
\u3000\u3000cot\uff08\u03c0\uff0b\u03b1\uff09= cot\u03b1
\u3000\u3000\u516c\u5f0f\u4e09\uff1a
\u3000\u3000\u4efb\u610f\u89d2\u03b1\u4e0e -\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
\u3000\u3000sin\uff08-\u03b1\uff09= -sin\u03b1
\u3000\u3000cos\uff08-\u03b1\uff09= cos\u03b1
\u3000\u3000tan\uff08-\u03b1\uff09= -tan\u03b1
\u3000\u3000cot\uff08-\u03b1\uff09= -cot\u03b1
\u3000\u3000\u516c\u5f0f\u56db\uff1a
\u3000\u3000\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
\u3000\u3000sin\uff08\u03c0-\u03b1\uff09= sin\u03b1
\u3000\u3000cos\uff08\u03c0-\u03b1\uff09= -cos\u03b1
\u3000\u3000tan\uff08\u03c0-\u03b1\uff09= -tan\u03b1
\u3000\u3000cot\uff08\u03c0-\u03b1\uff09= -cot\u03b1
\u3000\u3000\u516c\u5f0f\u4e94\uff1a
\u3000\u3000\u5229\u7528\u516c\u5f0f-\u548c\u516c\u5f0f\u4e09\u53ef\u4ee5\u5f97\u52302\u03c0-\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
\u3000\u3000sin\uff082\u03c0-\u03b1\uff09= -sin\u03b1
\u3000\u3000cos\uff082\u03c0-\u03b1\uff09= cos\u03b1
\u3000\u3000tan\uff082\u03c0-\u03b1\uff09= -tan\u03b1
\u3000\u3000cot\uff082\u03c0-\u03b1\uff09= -cot\u03b1
\u3000\u3000\u516c\u5f0f\u516d\uff1a
\u3000\u3000\u03c0/2\u00b1\u03b1\u53ca3\u03c0/2\u00b1\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
\u3000\u3000sin\uff08\u03c0/2+\u03b1\uff09= cos\u03b1
\u3000\u3000cos\uff08\u03c0/2+\u03b1\uff09= -sin\u03b1
\u3000\u3000tan\uff08\u03c0/2+\u03b1\uff09= -cot\u03b1
\u3000\u3000cot\uff08\u03c0/2+\u03b1\uff09= -tan\u03b1
\u3000\u3000sin\uff08\u03c0/2-\u03b1\uff09= cos\u03b1
\u3000\u3000cos\uff08\u03c0/2-\u03b1\uff09= sin\u03b1
\u3000\u3000tan\uff08\u03c0/2-\u03b1\uff09= cot\u03b1
\u3000\u3000cot\uff08\u03c0/2-\u03b1\uff09= tan\u03b1
\u3000\u3000sin\uff083\u03c0/2+\u03b1\uff09= -cos\u03b1
\u3000\u3000cos\uff083\u03c0/2+\u03b1\uff09= sin\u03b1
\u3000\u3000tan\uff083\u03c0/2+\u03b1\uff09= -cot\u03b1
\u3000\u3000cot\uff083\u03c0/2+\u03b1\uff09= -tan\u03b1
\u3000\u3000sin\uff083\u03c0/2-\u03b1\uff09= -cos\u03b1
\u3000\u3000cos\uff083\u03c0/2-\u03b1\uff09= -sin\u03b1
\u3000\u3000tan\uff083\u03c0/2-\u03b1\uff09= cot\u03b1
\u3000\u3000cot\uff083\u03c0/2-\u03b1\uff09= tan\u03b1
\u3000\u3000(\u4ee5\u4e0ak\u2208Z)
\u3000\u3000\u8fd9\u4e2a\u7269\u7406\u5e38\u7528\u516c\u5f0f\u6211\u8d39\u4e86\u534a\u5929\u7684\u52b2\u624d\u8f93\u8fdb\u6765,\u5e0c\u671b\u5bf9\u5927\u5bb6\u6709\u7528
\u3000\u3000A\u00b7sin(\u03c9t+\u03b8)+ B\u00b7sin(\u03c9t+\u03c6) =
\u3000\u3000\u221a{(A^2 +B^2 +2ABcos(\u03b8-\u03c6)} �6�1 sin{ \u03c9t + arcsin[ (A�6�1sin\u03b8+B�6�1sin\u03c6) / \u221a{A^2 +B^2; +2ABcos(\u03b8-\u03c6)} }
\u3000\u3000\u221a\u8868\u793a\u6839\u53f7,\u5305\u62ec{\u2026\u2026}\u4e2d\u7684\u5185\u5bb9
\u9ad8\u4e2d\u6570\u5b66\uff1a\u5df2\u77e5\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u4e24\u4e2a\u6839\u4e3atana\u548ctanb\uff0c\u6c42tan\uff08a+b\uff09
tan（2kπ+α）=tan α
tan(π/2-α）=cot α
tan（π/2+α）=-cot α
tan（π+α）=tan α
tan（π-α）=-tan α tan（α+β）=(tanα+tanβ）/（1-tanα·tanβ）
tan（α-β）=(tanα-tanβ）/（1+tanα·tanβ）
tan(a+b+c)=tanα+tanb+tanc-tanatanbtanc/1-tanatanb-tanctanb-tanatanc
绛旓細tan=sin/cos 锛坈os鈮0锛夈傦紙1锛夊湪鐩磋涓夎褰腑锛屸垹伪锛堜笉鏄洿瑙掞級鐨勫杈逛笌鏂滆竟鐨勬瘮鍙仛鈭犖辩殑姝ｅ鸡锛岃浣渟in伪锛屽嵆sin伪=鈭犖辩殑瀵硅竟/鈭犖辩殑鏂滆竟 銆傦紙2锛変綑寮︼紙浣欏鸡鍑芥暟锛夛紝涓夎鍑芥暟鐨勪竴绉嶃傚湪Rt鈻矨BC锛堢洿瑙掍笁瑙掑舰锛変腑锛屸垹C=90掳锛屸垹A鐨勪綑寮︽槸瀹冪殑閭昏竟姣斾笁瑙掑舰鐨勬枩杈癸紝鍗砪osA=b/c锛屼篃鍙...
绛旓細tanx鐨勫叕寮锛歵anx=sinx/cosx锛屾鍒囧嚱鏁tan胃=y/x銆傛鍒囧兼槸鎸囨槸鐩磋涓夎褰腑锛屾煇涓閿愯鐨勫杈逛笌鍙︿竴鐩搁偦鐩磋杈圭殑姣斿笺傚浜庝换鎰忎竴涓疄鏁皒锛岄兘瀵瑰簲鐫鍞竴鐨勮锛岃岃繖涓鍙堝搴旂潃鍞竴纭畾鐨勬鍒囧紅anx涓庡畠瀵瑰簲锛屾寜鐓ц繖涓搴旀硶鍒欏缓绔嬬殑鍑芥暟绉颁负姝ｅ垏鍑芥暟銆
绛旓細鍗婅鍏紡 tan(伪/2)=sin伪/(1+cos伪)=(1-cos伪)/sin伪銆傚嶈鍏紡 tan2伪=(2tan伪)/(1-tan伪^2)銆傞檷骞傚叕寮 tan^2(伪)=(1-cos(2伪))/(1+cos(2伪))銆備竾鑳藉叕寮 tan伪=2tan(伪/2)/[1-tan^2(伪/2)]銆備袱瑙掑拰涓庡樊鍏紡 tan(伪+尾)=(tan伪+tan尾)/(1-tan伪tan尾)銆倀an(...
绛旓細姹tan鐨勫叕寮涓猴細tana=y/x锛堢洿瑙掍笁瑙掑舰楂橀櫎浠ョ洿瑙掍笁瑙掑舰搴曡竟锛夛紝鍏朵腑鐩磋涓夎褰箣搴曚负x锛岄珮涓簓锛屾枩杈逛负z锛屽簳涓庢枩杈逛箣闂寸殑澶硅涓篴銆傛鍒囧嚱鏁版槸瑙捨稿湪浠绘剰鐩磋涓夎褰腑锛屼笌胃鐩稿搴旂殑瀵硅竟涓庨偦杈圭殑姣斿煎彨鍋氭鍒囥傝嫢灏單告斁鍦ㄧ洿瑙掑潗鏍囩郴涓嵆tan胃=y/x銆倀anA=鈭燗鐨勫杈/鈭燗瀵硅竟鐨勯偦杈广傚湪鐩磋鍧愭爣绯...
绛旓細tana=sina/cosa tan伪=1/cot伪 鍦ㄧ洿瑙掍笁瑙掑舰涓紝浠绘剰涓閿愯鈭燗鐨勫杈逛笌鏂滆竟鐨勬瘮鍙綔鈭燗鐨勬寮︼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=鈭燗鐨勫杈/鏂滆竟銆傚拰瑙鍏紡锛歴in ( 伪 卤 尾 ) = sin伪 路 cos尾 卤 cos伪 路 sin尾 sin ( 伪 + 尾 + 纬 ) = sin伪 路 cos尾 路 cos...
绛旓細鍗婅鍏紡銆tan(伪锛2)=sin伪锛忥紙1+cos伪锛夛紳(1-cos伪锛夛紡sin伪銆傚嶈鍏紡銆倀an2伪锛濓紙2tan伪锛夛紡(1-tan伪锛2)銆傞檷骞傚叕寮忋倀an^2(伪锛夛紳(1-cos(2伪锛夛級/(1+cos(2伪锛夛級銆備竾鑳藉叕寮忋倀an伪锛2tan(伪锛2)/銆備袱瑙掑拰涓庡樊鍏紡銆倀an(伪锛嬑诧級锛(tan伪锛媡an尾锛夛紡(1-tan伪tan尾锛夈...
绛旓細tan璁＄畻鍏紡鏄痶ana=y/x锛岀洿瑙掍笁瑙掑舰涔嬪簳涓簒锛岄珮涓簓锛屾枩杈逛负z锛屽簳涓庢枩杈逛箣闂寸殑澶硅涓篴銆倀an涓鑸寚姝ｅ垏锛屽湪Rt鈻矨BC涓紝鈭燙=90掳锛孉B鏄垹C鐨勫杈筩锛孊C鏄垹A鐨勫杈筧锛孉C鏄垹B鐨勫杈筨锛屾鍒囧嚱鏁板氨鏄痶anB=b/a锛屽嵆tanB=AC/BC銆備换鎰忚缁堣竟涓婇櫎椤剁偣澶栫殑浠讳竴鐐圭殑妯潗鏍囬櫎浠ヨ鐐圭殑闈為浂绾靛潗鏍囷紝瑙...
绛旓細tan(伪/2)=sin伪/(1+cos伪)=(1-cos伪)/sin伪 鍊嶈鍏紡 tan2伪=(2tan伪)/(1-tan伪^2)闄嶅箓鍏紡 tan^2(伪)=(1-cos(2伪))/(1+cos(2伪))涓囪兘鍏紡 tan伪=2tan(伪/2)/[1-tan^2(伪/2)]涓よ鍜屼笌宸叕寮 tan(伪+尾)=(tan伪+tan尾)/(1-tan伪tan尾)tan(伪-尾)=(tan伪-...
绛旓細=tan伪tan(伪+尾) =锛坱an伪+tan尾锛/锛1-tan伪脳tan尾锛塼an(伪-尾) =锛坱an伪-tan尾锛/锛1+tan伪脳tan尾锛塼an(蟺/2+伪)=锛峜ot伪tan(蟺/2锛嵨)=cot伪 璇卞鍏紡鏄寚涓夎鍑芥暟涓紝鍒╃敤鍛ㄦ湡鎬у皢瑙掑害姣旇緝澶х殑涓夎鍑芥暟锛岃浆鎹负瑙掑害姣旇緝灏忕殑涓夎鍑芥暟鐨勫叕寮銆 璇卞鍏紡鏈夊叚缁勶紝鍏54涓
绛旓細涓夎鍑芥暟tan鐨勫叕寮锛歵an(A+B)=(tanA+tanB)/(1-tanAtanB)銆備笁瑙掑嚱鏁板叕寮忕湅浼煎緢澶氥佸緢澶嶆潅锛屼絾鍙鎺屾彙浜嗕笁瑙掑嚱鏁扮殑鏈川鍙婂唴閮ㄨ寰嬶紝灏变細鍙戠幇涓夎鍑芥暟鍚勪釜鍏紡涔嬮棿鏈夊己澶х殑鑱旂郴锛岃屾帉鎻′笁瑙掑嚱鏁扮殑鍐呴儴瑙勫緥鍙婃湰璐ㄤ篃鏄濂戒笁瑙掑嚱鏁扮殑鍏抽敭鎵鍦ㄣ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婂嚱鏁扮殑鍑芥暟銆傚畠浠殑鏈川鏄...
