三角函数公式 高中三角函数公式
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两角和公式sin(A+B) = sinAcosB+cosAsinB
sin(A-B) = sinAcosB-cosAsinB
cos(A+B) = cosAcosB-sinAsinB
cos(A-B) = cosAcosB+sinAsinB
tan(A+B) =tanAtanB-1tanBtanA+
tan(A-B) =tanAtanB1tanBtanA+
cot(A+B) =cotAcotB1-cotAcotB+
cot(A-B) =cotAcotB1cotAcotB +
倍角公式
tan2A =Atan12tanA2 Sin2A=2SinA CosA
Cos2A = Cos2A-Sin2A=2Cos2A-1=1-2sin2A
三倍角公式
sin3A = 3sinA-4(sinA)3
cos3A = 4(cosA)3-3cosA
tan3a = tana·tan(3π+a)·tan(3π-a)
半角公式
sin(2A)=2cos1A cos(2A)=2cos1A+
tan(2A)=AAcos1cos1+ cot(2A)=AAcos1cos1 +
tan(2A)=AAsincos1 =AAcos1sin+
和差化积和差化积和差化积和差化积
sina+sinb=2sin2ba+cos2ba
sina-sinb=2cos2ba+sin2ba cosa+cosb = 2cos2ba+cos2ba cosa-cosb = -2sin2ba+sin2ba tana+tanb=babacoscos)sin(+ 积化和差
sinasinb = -21[cos(a+b)-cos(a-b)]
cosacosb = 21[cos(a+b)+cos(a-b)]
sinacosb = 21[sin(a+b)+sin(a-b)]
cosasinb = 21[sin(a+b)-sin(a-b)]
诱导公式
sin(-a) = -sina
cos(-a) = cosa
sin(2π-a) = cosa
cos(2π-a) = sina
sin(2π+a) = cosa
cos(2π+a) = -sina
sin(π-a) = sina
cos(π-a) = -cosa
sin(π+a) = -sina
cos(π+a) = -cosa
tgA=tanA =aacossin
万能公式
sina=2)2(tan12tan2aa+
cosa=22)2(tan1)2(tan1aa+
tana=2)2(tan12tan2aa
其它公式
a sina+b cosa=)b(a22+×sin(a+c) [其中tanc=ab] a sin(a)-b cos(a) = )b(a22+×cos(a-c) [其中tan(c)=ba] 1+sin(a) =(sin2a+cos2a)2 1-sin(a) = (sin2a-cos2a)2
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绛旓細涓夎鍑芥暟鍏紡鏄敤浜庢弿杩颁笁瑙掑嚱鏁颁箣闂寸殑鍏崇郴鐨勬暟瀛﹀叕寮忋備互涓嬫槸涓浜涘父瑙佺殑涓夎鍑芥暟鍏紡鍙婂叾鍚箟锛1. 姝ｅ鸡鍑芥暟鍏紡锛歴in^2(x) + cos^2(x) = 1銆傝繖涓叕寮忕О涓烘寮﹀嚱鏁扮殑骞虫柟鍔犱綑寮﹀嚱鏁扮殑骞虫柟绛変簬1鐨勬亽绛夊紡銆傚畠琛ㄧず鍦ㄤ换浣曡搴 x 涓婏紝姝ｅ鸡鍑芥暟鐨勫钩鏂逛笌浣欏鸡鍑芥暟鐨勫钩鏂逛箣鍜屾绘槸绛変簬1銆2. 浣欏鸡鍑芥暟鍏紡锛...
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绛旓細5銆佷簩鍊嶈鍏紡锛圖ouble-Angle Formula锛夛細sin锛2x锛=2sin锛坸锛塩os锛坸锛夈傝繖涓叕寮忕敤浜庤绠椾竴涓搴︾殑涓ゅ嶇殑姝ｅ鸡鍊笺傞氳繃杩欎釜鍏紡锛屾垜浠彲浠ュ皢涓涓搴︾殑姝ｅ鸡鍊煎垎瑙ｄ负涓や釜瑙掑害鐨勬寮﹀煎拰浣欏鸡鍊肩殑涔樼Н銆涓夎鍑芥暟鐨勬ц川锛1銆佸懆鏈熸э細涓夎鍑芥暟鐨勪竴涓噸瑕佹ц川鏄畠浠殑鍛ㄦ湡鎬с傚浜庢寮﹀嚱鏁帮紙sin锛夊拰浣欏鸡鍑芥暟...
绛旓細涓夎鍑芥暟鍏紡锛歴in(伪锛嬑诧級=sin伪cos尾锛媍os伪sin尾銆俿in(伪锛嵨诧級=sin伪cos尾锛峜os伪sin尾銆俢os(伪锛嬑诧級=cos伪cos尾锛峴in伪sin尾銆俢os(伪锛嵨诧級=cos伪cos尾锛媠in伪sin尾銆倀an(伪锛嬑诧級=(tan伪锛媡an尾锛/(1-tan伪tan尾锛夈倀an(伪锛嵨诧級=(tan伪锛峵an尾锛/(1+tan伪tan尾锛夈俢os...
绛旓細涓夎鍑芥暟鍏紡鏈夌Н鍖栧拰宸叕寮忋佸拰宸寲绉叕寮忋佷笁鍊嶈鍏紡銆佹寮︿簩鍊嶈鍏紡銆佷綑寮︿簩鍊嶈鍏紡銆佷綑寮﹀畾鐞嗙瓑銆1绉寲鍜屽樊鍏紡銆俿in伪路cos尾=(1/2)*[sin(伪+尾)+sin(伪-尾)]锛沜os伪路sin尾=(1/2)*[sin(伪+尾)-sin(伪-尾)];cos伪路cos尾=(1/2)*[cos(伪+尾)+cos(伪-尾)];sin伪路...
绛旓細鍏紡涓簊inA=a/c锛宑osA=b/c锛宼anA=a/b銆傚湪鐩磋涓夎褰腑锛屽綋骞抽潰涓婄殑涓夌偣A銆丅銆丆鐨勮繛绾匡紝AB銆丄C銆丅C锛屾瀯鎴愪竴涓洿瑙掍笁瑙掑舰锛屽叾涓垹ACB涓虹洿瑙掋傚鈭燘AC鑰岃█锛屽杈筧=BC銆佹枩杈筩=AB銆侀偦杈筨=AC銆
绛旓細涓銆乻in搴︽暟鍏紡 1銆乻in 30= 1/2銆2銆乻in 45=鏍瑰彿2/2銆3銆乻in 60= 鏍瑰彿3/2銆備簩銆乧os搴︽暟鍏紡 1銆乧os 30=鏍瑰彿3/2銆2銆乧os 45=鏍瑰彿2/2銆3銆乧os 60=1/2銆備笁銆乼an搴︽暟鍏紡 1銆乼an 30=鏍瑰彿3/3銆2銆乼an 45=1銆3銆乼an 60=鏍瑰彿3銆涓夎鍑芥暟涓昏杩愮敤鏂规硶锛氫笁瑙掑嚱鏁颁互瑙掑害锛堟暟瀛︿笂鏈...
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婂嚱鏁扮殑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...
绛旓細甯歌涓夎鍑芥暟鍏紡鐩稿叧鍐呭濡備笅锛1銆佹亽绛夊紡锛歴in^2锛坸锛+cos^2锛坸锛=1锛岃繖鏄熀浜庡嬀鑲″畾鐞嗙殑涓涓熀鏈亽绛夊紡銆2銆佸拰瑙掑叕寮忥細sin锛坸+ y锛=sin锛坸锛塩os锛坹锛+cos锛坸锛塻in锛坹锛夛紝cos锛坸+ y锛=cos锛坸锛塩os锛坹锛-sin锛坸锛塻in锛坹锛夈傝繖浜涘叕寮忓彲浠ョ敤浜庤绠椾袱涓搴︾殑鍜岀殑姝ｅ鸡鎴栦綑寮︺3銆佸樊瑙...
