目錄高中數學92個公式全總結 高中數學基礎公式匯總 高考數學必考公式歸納 高中必背88個數學公式 因式分解23個公式
楂樹竴鏁板?﹀繀鑳屽叕寮忓?備笅錛?
璇卞?煎叕寮忋??
涓?錛氳?疚變負浠繪剰瑙掕儭紼匡紝緇堣竟鐩稿悓鐨勮?掔殑鍚屼竴涓夎?掑嚱鏁扮殑鍊肩浉絳夛細
sin(2k蟺+偽)=sin偽(k鈭圸)cos(2k蟺+偽)=cos偽(k鈭圸)tan(2k蟺+偽)=tan偽(k鈭圸)cot(2k蟺+偽)=cot偽(k鈭圸)銆?
浜岋細璁疚變負浠繪剰瑙掞紝蟺+偽鐨勪笁瑙掑嚱鏁板?間笌偽鐨勪笁瑙掑嚱鏁板?間箣闂寸殑鍏崇郴錛?
sin(蟺+偽)=-sin偽cos(蟺+偽)=-cos偽tan(蟺+偽)=tan偽cot(蟺+偽)=cot偽銆?
涓夛細浠繪剰瑙捨變笌-偽鐨勪笁瑙掑嚱鏁板?間箣闂寸殑鍏崇郴錛?
sin(-偽)=-sin偽cos(-偽)=cos偽tan(-偽)=-tan偽cot(-偽)=-cot偽銆?
鍥涳細鍒╃敤鍏?寮忎簩鍜屽叕寮忎笁鍙?浠ュ緱鍒跋?-偽涓幬辯殑涓夎?掑嚱鏁板?艱￥妗ｅ瓭涔嬮棿鐨勫叧緋伙細
sin(蟺-偽)=sin偽cos(蟺-偽)=-cos偽tan(蟺-偽)=-tan偽cot(蟺-偽)=-cot偽銆?
浜旓細鍒╃敤鍏?寮忎竴鍜屽叕寮忎笁鍙?浠ュ緱鍒?2蟺-偽涓幬辯殑涓夎?掑嚱鏁板?間箣闂寸殑鍏崇郴錛?
sin(2蟺-偽)=-sin偽cos(2蟺-偽)=cos偽tan(2蟺-偽)=-tan偽cot(2蟺-偽)=-cot偽銆?
楂樹竴鏁板?﹀叕寮忋??
鏌愪簺鏁板垪鍓峮欏瑰拰銆?
1+2+3+4+5+6+7+8+9++n=n(n+1)/21+3+5+7+9+11+13+15++(2n-1)=n2銆?
2+4+6+8+10+12+14++(2n)=n(n+1)12+22+32+42+52+62+72+82++n2=n(n+1)(2n+1)/6銆?
13+23+33+43+53+63+n3=n2(n+1)2/41_2+2_3+3_4+4_5+5_6+6_7++n(n+1)=n(n+1)(n+2)/3銆?
姝ｅ雞瀹氱悊a/sina=b/sinb=c/sinc=2r娉?錛氬叾涓璻琛ㄧず涓夎?掑艦鐨勫?栨帴鍦嗗崐寰勩??
浣欏雞瀹氱悊b2=a2+c2-2accosb娉?錛氳?抌鏄?杈筧鍜岃竟c鐨勫す瑙掋??
鍦嗙殑鏍囧噯鏂圭▼(x-a)2+(y-b)2=r2娉?錛?(a錛宐)鏄?鍦嗗績鍧愭爣銆傝牏鏃?
鍦嗙殑涓?鑸?鏂圭▼x2+y2+dx+ey+f=0娉?錛歞2+e2-4f0銆?
鎶涚墿綰挎爣鍑嗘柟紼媦2=2pxy2=-2p_2=2pyx2=-2py銆?
姝ｆ１閿ヤ晶闈㈢Нs=1/2c_h姝ｆ１鍙頒晶闈㈢Нs=1/2(c+c)h銆?
蹇呭?囧叕寮忓?備笅錛?
y=ax*+bx+c
灝辨槸y絳変簬ax鐨勫鉤鏂瑰姞涓奲x鍐嶅姞涓奵
a>0鏃跺紑鍙ｅ悜涓?
a<0鏃跺紑鍙ｅ悜涓?
c=0鏃舵姏鐗╃嚎緇忚繃鍘熺偣
b=0鏃舵姏鐗╃嚎搴嗗敜瀵圭О杞翠負y杞?
榪樻湁欏剁偣寮弝=a錛坸+h錛?*+k
灝辨槸y絳変簬a涔樹互錛坸+h錛夌殑騫蟲柟+k
-h鏄?欏剁偣鍧愭爣鐨剎
k鏄?欏剁偣鍧愭爣鐨剏
涓?鑸?鐢ㄤ簬姹傛渶澶у?間笌鏈?灝忓??
鎶涚墿綰挎爣鍑嗗洶鍧︽柟紼?:y^2=2px
瀹冭〃紺烘姏鐗╃嚎鐨勭劍鐐瑰湪x鐨勬?ｅ崐杞翠笂,鐒︾偣鍧愭爣涓?(p/2,0)鍑嗙嚎鏂圭▼涓簒=-p/2
鐢變簬鎶涚墿綰跨殑鐒︾偣鍙?鍦ㄤ換鎰忓崐杞磋獕灝哄嚡,鏁呭叡鏈夋爣鍑嗘柟紼媦^2=2pxy^2=-2pxx^2=2pyx^2=-2py
涓?銆乻inh-1 x dx = x sinh-1 x-+ C
浜屻?乧osh-1 x dx = x cosh-1 x-+ C
涓夈?乼anh-1 x dx = x tanh-1 x+ ln | 1-x2|+ C
鍥涖?侀ゥ鏄ョ?癱oth-1 x dx = x coth-1 x- ln | 1-x2|+ C
浜斻?乻ech-1 x dx = x sech-1 x- sin-1 x + C
鍏?鐑傝皥銆乧sch-1 x dx = x csch-1 x+ sinh-1 x + C
涓冦?乻in 3胃=3sin胃-4sin3胃
鍏?銆乧os3胃=4cos3胃-3cos胃
涔濄?佲啋sin3胃= (3sin胃-sin3胃)
鍗併?佲啋cos3胃= (3cos胃+cos3胃)
鍗佷竴銆乻in (偽鹵尾)=sin 偽 cos 尾 鹵 cos 偽 sin 尾
鍗佷簩銆乧os (偽鹵尾)=cos 偽 cos 尾 sin 偽 sin 尾
鍗佷笁銆?2 sin 偽 cos 尾 = sin (偽+尾) + sin (偽-尾)
鍗佸洓銆?2 cos 偽 sin 尾 = sin (偽+尾) - sin (偽-尾)
鍗佷簲銆?2 cos 偽 cos 尾 = cos (偽-尾) + cos (偽+尾)
鍗佸叚銆?2 sin 偽 sin 尾 = cos (偽-尾) - cos (偽+尾)
鍗佷竷銆乻in 偽 + sin 尾 = 2 sin (偽+尾) cos (偽-尾)
鍗佸叓銆乻in 偽 - sin 尾 = 2 cos (偽+尾) sin (偽-尾)
鍗佷節銆乧os 偽 + cos 尾 = 2 cos (偽+尾) cos (偽-尾)
浜屽崄銆佹．榪筩os 偽 - cos 尾 = -2 sin (偽+尾) sin (偽-尾)
楂樹腑蹇呰儗88涓?鏁板?﹀叕寮忔湁錛氬渾鐨勫叕寮忋??妞?鍦嗗叕寮?銆佷袱瑙掑拰鍏?寮忋??鍊嶈?掑叕寮?銆佸崐瑙掑叕寮忋?佸拰宸?鍖栫Н銆?絳夊樊鏁板垪銆佺瓑姣旀暟鍒椼?佹姏鐗╃嚎絳夊叕寮忋??
涓?銆侀珮涓?蹇呰儗88涓?鏁板?﹀叕寮忊?斺?斿渾鐨勫叕寮?
1銆佸渾浣撶Н=4/3(pi)(r^3)
2銆侀潰縐?=(pi)(r^2)
3銆佸懆闀?=2(pi)r
4銆?鍦嗕婦鍙嬬殑鏍囧噯鏂圭▼(x-a)2+(y-b)2=r2銆?(a,b)鏄?鍦嗗績鍧愭爣銆?
5銆?鍦嗙殑涓?鑸?鏂圭▼x2+y2+dx+ey+f=0銆恉2+e2-4f>0銆?
浜屻?侀珮涓?蹇呰儗88涓?鏁板?﹀叕寮忊?斺?旀き鍦嗗叕寮?
1銆?妞?鍦嗗懆闀?鍏?寮忥細l=2蟺b+4(a-b)
2銆佹き鍦嗗懆闀垮畾鐞嗭細妞?鍦嗙殑鍛ㄩ暱絳変簬璇ユき鍦嗙煭鍗婅醬錛岄暱涓哄崐寰勭殑鍦嗗懆闀?(2蟺b)鍔犱笂鍥涘?嶇殑璇ユき鍦嗛暱鍗婅醬闀?(a)涓庣煭鍗婅醬闀?(b)鐨勫樊.
3銆?妞?鍦嗛潰縐?鍏?寮?錛歴=蟺ab
4銆佹き鍦嗛潰縐?瀹氳繜鎼虹悊錛氭き鍦嗙殑闈㈢Н絳変簬鍦嗗懆鐜?(蟺)涔樿?ユき鍦嗛暱鍗婅醬闀?(a)涓庣爜絳斾紡鐭?鍗婅醬闀?(b)鐨勪箻縐?銆?
浠ヤ笂妞?鍦嗗懆闀褲?侀潰縐?鍏?寮忎腑铏界劧娌℃湁鍑虹幇妞?鍦嗗懆鐜噒,浣嗚繖涓や釜鍏?寮忛兘鏄?閫氳繃妞?鍦嗗懆鐜噒鎺ㄥ?兼紨鍙樿?屾潵銆?
涓夈?侀珮涓?蹇呰儗88涓?鏁板?﹀叕寮忊?斺?斾袱瑙掑拰鍏?寮?
1銆乻in(a+b)=sinacosb+cosasinbsin(a-b)=sinacosb-sinbcosa
2銆乧os(a+b)=cosacosb-sinasinbcos(a-b)=cosacosb+sinasinb
3銆乼an(a+b)=(tana+tanb)/(1-tanatanb)tan(a-b)=(tana-tanb)/(1+tanatanb)
4銆乧tg(a+b)=(ctgactgb-1)/(ctgb+ctga)ctg(a-b)=(ctgactgb+1)/(ctgb-ctga)
鍥涖?侀珮涓?蹇呰儗88涓?鏁板?﹀叕寮忊?斺?斿?嶈?掑叕寮?
1銆乼an2a=2tana/(1-tan2a)ctg2a=(ctg2a-1)/2ctga
2銆乧os2a=cos2a-sin2a=2cos2a-1=1-2sin2a
銆?銆?楂樹腑鏁板?﹀叕寮忔槸楂樿?冩暟瀛﹀?嶄範鑷沖叧閲嶈?佺殑鐭ヨ瘑鐐癸紝涓轟簡甯?鍔╅珮涓夎?冪敓榪涜?岄珮鑰冩暟瀛︾殑澶嶄範銆備笅闈㈡垜緇欎綘鍒嗕韓楂樹腑蹇呰儗鏁板?﹀叕寮忥紝嬈㈣繋闃呰?匯??
銆?銆? 楂樹腑蹇呰儗鏁板?﹀叕寮忥細涓?鍏冧簩嬈℃柟紼嬬殑瑙?
銆?銆?-b+√(b2-4ac)/2a-b-√(b2-4ac)/2a
銆?銆?鏍逛笌緋繪暟鏃忓瞾鍩圭殑鍏崇郴x1+x2=-b/ax1*x2=c/a娉?錛氶煢杈懼畾鐞?
銆?銆?鍒ゅ埆寮廱2-4a=0娉?錛氭柟紼嬫湁鐩哥瓑鐨勪袱瀹炴牴
銆?銆?b2-4ac>0娉?錛氭柟紼嬫湁涓や釜涓嶇浉絳夌殑涓?瀹炴牴
銆?銆?b2-4ac<0娉?錛氭柟紼嬫湁鍏辮江澶嶆暟鏍?
銆? 銆?楂樹腑蹇呰儗鏁板?﹀叕寮忥細绔嬩綋鍥懼艦鍙婂鉤闈㈠浘褰㈢殑鍏?寮?
銆?銆?鍦嗙殑鏍囧噯鏂圭▼(x-a)2+(y-b)2=r2娉?錛?(a,b)鏄?鍦嗗績鍧愭爣
銆?銆?鍦嗙殑涓?鑸?鏂圭▼x2+y2+Dx+Ey+F=0娉?錛欴2+E2-4F>0
銆?銆?鎶涚墿綰挎爣鍑嗘柟紼媦2=2pxy2=-2pxx2=2pyx2=-2py
銆?銆?鐩存１鏌變晶闈㈢НS=c*h鏂滄１鏌變晶闈㈢НS=c'*h
銆?銆?姝ｆ１閿ヤ晶闈㈢НS=1/2c*h'姝ｆ１鍙頒晶闈㈢НS=1/2(c+c')h'
銆?銆?鍦嗗彴渚ч潰縐疭=1/2(c+c')l=pi(R+r)l鐞冪殑琛ㄩ潰縐疭=4pi*r2
銆?銆?鍦嗘煴渚ч潰縐疭=c*h=2pi*h鍦嗛敟渚ч潰縐疭=1/2*c*l=pi*r*l
銆?銆?寮ч暱鍏?寮弆=a*ra鏄?鍦嗗績瑙掔殑寮у害鏁皉>0鎵囧艦闈㈢Н鍏?寮弒=1/2*l*r
銆?銆?閿ヤ綋浣撶Н鍏?寮廣=1/3*S*H鍦嗛敟浣撲綋縐?鍏?寮廣=1/3*pi*r2h
銆?銆?鏂滄１鏌變綋縐疺=S'L娉?錛氬叾涓?,S'鏄?鐩存埅闈㈤潰縐?錛孡鏄?渚ф１闀?
銆?銆?鏌變綋浣撶Н鍏?寮廣=s*h鍦嗘煴浣揤=pi*r2h
銆?銆? 楂樹腑蹇呰儗鏁板?﹀叕寮忥細鍥懼艦鍛ㄩ暱銆侀潰縐?銆佷綋縐?鍏?寮?
銆?銆?闀挎柟褰㈢殑鍛ㄩ暱=(闀?+瀹?)×2
銆?銆?姝ｆ柟褰㈢殑鍛ㄩ暱=杈歸暱×4
銆?銆?闀挎柟褰㈢殑闈㈢Н=闀?×瀹?
銆?銆?姝ｆ柟褰㈢殑闈㈢Н=杈歸暱×杈歸暱
銆?銆?涓夎?掑艦鐨勯潰縐?
銆?銆?宸茬煡涓夎?掑艦搴昦錛岄珮h錛屽垯S=ah/2
銆?銆?宸茬煡涓夎?掑艦涓夎竟a,b,c,鍗婂懆闀縫,鍒橲=√[p(p-a)(p-b)(p-c)](嫻蜂雞鍏?寮?)(p=(a+b+c)/2)
銆?銆?鍜岋細(a+b+c)*(a+b-c)*1/4
銆?銆?宸茬煡涓夎?掑艦涓よ竟a,b,榪欎袱杈瑰す瑙扖錛屽垯S=absinC/2
銆?銆?璁句笁瑙掑艦涓夎竟鍒嗗埆涓篴銆乥銆乧錛屽唴鍒囧渾鍗婂緞涓簉
銆?銆?鍒欎笁瑙掑艦闈㈢Н=(a+b+c)r/2
銆?闆?娑層??璁句笁瑙掑艦涓夎竟鍒嗗埆涓篴銆佸厗鍞痓銆乧錛屽?栨帴鍦嗗崐寰勪負r
銆?銆?鍒欎笁瑙掑艦闈㈢Н=abc/4r
