高二数学公式有哪些 高二数学的所有公式
\u9ad8\u4e8c\u6570\u5b66\u516c\u5f0f\u6709\u54ea\u4e9b\uff1f\u5411\u91cf\u516c\u5f0f\uff1a
1.\u5355\u4f4d\u5411\u91cf\uff1a\u5355\u4f4d\u5411\u91cfa0=\u5411\u91cfa/|\u5411\u91cfa|
2.P(x,y) \u90a3\u4e48 \u5411\u91cfOP=x\u5411\u91cfi+y\u5411\u91cfj
|\u5411\u91cfOP|=\u6839\u53f7\uff08x\u5e73\u65b9+y\u5e73\u65b9\uff09
3.P1(x1,y1) P2(x2,y2)
\u90a3\u4e48\u5411\u91cfP1P2=\uff5bx2-x1,y2-y1\uff5d
|\u5411\u91cfP1P2|=\u6839\u53f7[(x2-x1)\u5e73\u65b9+(y2-y1)\u5e73\u65b9]
4.\u5411\u91cfa=\uff5bx1,x2\uff5d\u5411\u91cfb=\uff5bx2,y2\uff5d
\u5411\u91cfa*\u5411\u91cfb=|\u5411\u91cfa|*|\u5411\u91cfb|*Cos\u03b1=x1x2+y1y2
Cos\u03b1=\u5411\u91cfa*\u5411\u91cfb/|\u5411\u91cfa|*|\u5411\u91cfb|
(x1x2+y1y2)
= \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014
\u6839\u53f7(x1\u5e73\u65b9+y1\u5e73\u65b9)*\u6839\u53f7\uff08x2\u5e73\u65b9+y2\u5e73\u65b9\uff09
5.\u7a7a\u95f4\u5411\u91cf\uff1a\u540c\u4e0a\u63a8\u8bba
\uff08\u63d0\u793a\uff1a\u5411\u91cfa=\uff5bx,y,z\uff5d\uff09
6.\u5145\u8981\u6761\u4ef6\uff1a
\u5982\u679c\u5411\u91cfa\u22a5\u5411\u91cfb
\u90a3\u4e48\u5411\u91cfa*\u5411\u91cfb=0
\u5982\u679c\u5411\u91cfa//\u5411\u91cfb
\u90a3\u4e48\u5411\u91cfa*\u5411\u91cfb=\u00b1|\u5411\u91cfa|*|\u5411\u91cfb|
\u6216\u8005x1/x2=y1/y2
7.|\u5411\u91cfa\u00b1\u5411\u91cfb|\u5e73\u65b9
=|\u5411\u91cfa|\u5e73\u65b9+|\u5411\u91cfb|\u5e73\u65b9\u00b12\u5411\u91cfa*\u5411\u91cfb
=(\u5411\u91cfa\u00b1\u5411\u91cfb)\u5e73\u65b9
\u4e09\u89d2\u51fd\u6570\u516c\u5f0f\uff1a
1.\u4e07\u80fd\u516c\u5f0f
\u4ee4tan(a/2)=t
sina=2t/(1+t^2)
cosa=(1-t^2)/(1+t^2)
tana=2t/(1-t^2)
2.\u8f85\u52a9\u89d2\u516c\u5f0f
asint+bcost=(a^2+b^2)^(1/2)sin(t+r)
cosr=a/[(a^2+b^2)^(1/2)]
sinr=b/[(a^2+b^2)^(1/2)]
tanr=b/a
3.\u4e09\u500d\u89d2\u516c\u5f0f
sin(3a)=3sina-4(sina)^3
cos(3a)=4(cosa)^3-3cosa
tan(3a)=[3tana-(tana)^3]/[1-3(tana^2)]
4.\u79ef\u5316\u548c\u5dee
sina*cosb=[sin(a+b)+sin(a-b)]/2
cosa*sinb=[sin(a+b)-sin(a-b)]/2
cosa*cosb=[cos(a+b)+cos(a-b)]/2
sina*sinb=-[cos(a+b)-cos(a-b)]/2
5.\u79ef\u5316\u548c\u5dee
sina+sinb=2sin[(a+b)/2]cos[(a-b)/2]
sina-sinb=2sin[(a-b)/2]cos[(a+b)/2]
cosa+cosb=2cos[(a+b)/2]cos[(a-b)/2]
cosa-cosb=-2sin[(a+b)/2]sin[(a-b)/2]
1.\u4e07\u80fd\u516c\u5f0f
\u4ee4tan(a/2)=t
sina=2t/(1+t^2)
cosa=(1-t^2)/(1+t^2)
tana=2t/(1-t^2)
2.\u8f85\u52a9\u89d2\u516c\u5f0f
asint+bcost=(a^2+b^2)^(1/2)sin(t+r)
cosr=a/[(a^2+b^2)^(1/2)]
sinr=b/[(a^2+b^2)^(1/2)]
tanr=b/a
3.\u4e09\u500d\u89d2\u516c\u5f0f
sin(3a)=3sina-4(sina)^3
cos(3a)=4(cosa)^3-3cosa
tan(3a)=[3tana-(tana)^3]/[1-3(tana^2)]
4.\u79ef\u5316\u548c\u5dee
sina*cosb=[sin(a+b)+sin(a-b)]/2
cosa*sinb=[sin(a+b)-sin(a-b)]/2
cosa*cosb=[cos(a+b)+cos(a-b)]/2
sina*sinb=-[cos(a+b)-cos(a-b)]/2
5.\u79ef\u5316\u548c\u5dee
sina+sinb=2sin[(a+b)/2]cos[(a-b)/2]
sina-sinb=2sin[(a-b)/2]cos[(a+b)/2]
cosa+cosb=2cos[(a+b)/2]cos[(a-b)/2]
cosa-cosb=-2sin[(a+b)/2]sin[(a-b)/2]
\u5148\u7ed9\u8fd9\u4e9b\u5427!\u6bd5\u7adf\u4e09\u89d2\u51fd\u6570\u53d8\u6362\u6700\u590d\u6742.
\u8fd9\u662f\u6211\u81ea\u5df1\u603b\u7ed3\u7684\uff0c\u597d\u7d2f\u5440\uff01(\u5f53\u5e74\u81ea\u5df1\u90fd\u8bc1\u8fc7)
令tan(a/2)=t
sina=2t/(1+t^2)
cosa=(1-t^2)/(1+t^2)
tana=2t/(1-t^2)
2.辅助角公式
asint+bcost=(a^2+b^2)^(1/2)sin(t+r)
cosr=a/[(a^2+b^2)^(1/2)]
sinr=b/[(a^2+b^2)^(1/2)]
tanr=b/a
3.三倍角公式
sin(3a)=3sina-4(sina)^3
cos(3a)=4(cosa)^3-3cosa
tan(3a)=[3tana-(tana)^3]/[1-3(tana^2)]
4.积化和差
sina*cosb=[sin(a+b)+sin(a-b)]/2
cosa*sinb=[sin(a+b)-sin(a-b)]/2
cosa*cosb=[cos(a+b)+cos(a-b)]/2
sina*sinb=-[cos(a+b)-cos(a-b)]/2
5.积化和差
sina+sinb=2sin[(a+b)/2]cos[(a-b)/2]
sina-sinb=2sin[(a-b)/2]cos[(a+b)/2]
cosa+cosb=2cos[(a+b)/2]cos[(a-b)/2]
cosa-cosb=-2sin[(a+b)/2]sin[(a-b)/2]
向量公式:
1.单位向量:单位向量a0=向量a/|向量a|
2.P(x,y) 那么 向量OP=x向量i+y向量j
|向量OP|=根号(x平方+y平方)
3.P1(x1,y1) P2(x2,y2)
那么向量P1P2={x2-x1,y2-y1}
|向量P1P2|=根号[(x2-x1)平方+(y2-y1)平方]
4.向量a={x1,x2}向量b={x2,y2}
向量a*向量b=|向量a|*|向量b|*Cosα=x1x2+y1y2
Cosα=向量a*向量b/|向量a|*|向量b|
(x1x2+y1y2)
= ————————————————————
根号(x1平方+y1平方)*根号(x2平方+y2平方)
5.空间向量:同上推论
(提示:向量a={x,y,z})
6.充要条件:
如果向量a⊥向量b
那么向量a*向量b=0
如果向量a//向量b
那么向量a*向量b=±|向量a|*|向量b|
或者x1/x2=y1/y2
7.|向量a±向量b|平方
=|向量a|平方+|向量b|平方±2向量a*向量b
=(向量a±向量b)平方
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绛旓細涓夎鍑芥暟鍏紡锛1.涓囪兘鍏紡 浠an(a/2)=t sina=2t/(1+t^2)cosa=(1-t^2)/(1+t^2)tana=2t/(1-t^2)2.杈呭姪瑙掑叕寮 asint+bcost=(a^2+b^2)^(1/2)sin(t+r)cosr=a/[(a^2+b^2)^(1/2)]sinr=b/[(a^2+b^2)^(1/2)]tanr=b/a 3.涓夊嶈鍏紡 sin(3a)=3sina-4(...