高中数学公式大全 求高中数学公式大全
\u9ad8\u4e2d\u6570\u5b66\u516c\u5f0f\u5927\u51681\u3001\u96c6\u5408\u4e0e\u5e38\u7528\u903b\u8f91\u7528\u8bed
2\u3001 \u590d\u6570
3\u3001 \u5e73\u9762\u5411\u91cf
4\u3001 \u7b97\u6cd5\u3001\u63a8\u7406\u4e0e\u8bc1\u660e
5\u3001\u4e0d\u7b49\u5f0f\u3001\u7ebf\u6027\u89c4\u5212
6\u3001 \u8ba1\u6570\u539f\u7406\u4e0e\u4e8c\u9879\u5f0f\u5b9a\u7406
7\u3001 \u51fd\u6570\u3001\u57fa\u672c\u521d\u7b49\u51fd\u6570\u7684\u56fe\u50cf\u4e0e\u6027\u8d28
8\u3001\u51fd\u6570\u4e0e\u65b9\u7a0b\u3001\u51fd\u6570\u6a21\u578b\u53ca\u5176\u5e94\u7528
9\u3001\u5bfc\u6570\u53ca\u5176\u5e94\u7528
10\u3001\u4e09\u89d2\u51fd\u6570\u7684\u56fe\u5f62\u4e0e\u6027\u8d28
11\u3001\u4e09\u89d2\u6052\u7b49\u53d8\u5316\u4e0e\u89e3\u4e09\u89d2\u5f62
12\u3001\u7b49\u5dee\u6570\u5217\u3001\u7b49\u6bd4\u6570\u5217
13\u3001\u6570\u5217\u6c42\u548c\u53ca\u6570\u5217\u7684\u7b80\u5355\u5e94\u7528
14\u3001\u7a7a\u95f4\u51e0\u4f55\u4f53
15\u3001\u7a7a\u95f4\u70b9\u3001\u76f4\u7ebf\u3001\u5e73\u9762\u4f4d\u7f6e\u5173\u7cfb
16\u3001\u7a7a\u95f4\u5411\u91cf\u4e0e\u7acb\u4f53\u51e0\u4f55
17\u3001\u76f4\u7ebf\u4e0e\u5706\u7684\u65b9\u7a0b
18\u3001\u5706\u9525\u66f2\u7ebf\u7684\u5b9a\u4e49\u3001\u65b9\u7a0b\u4e0e\u6027\u8d28
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6-2020\u9ad8\u4e2d\u6570\u5b66\u5fc5\u5907\u516c\u5f0f\u5927\u5168
\u9ad8\u4e2d\u6570\u5b66\u5e38\u7528\u516c\u5f0f\u53ca\u5e38\u7528\u7ed3\u8bba
1. \u5143\u7d20\u4e0e\u96c6\u5408\u7684\u5173\u7cfb
, .
2.\u5fb7\u6469\u6839\u516c\u5f0f
.
3.\u5305\u542b\u5173\u7cfb
4.\u5bb9\u65a5\u539f\u7406
.
5\uff0e\u96c6\u5408 \u7684\u5b50\u96c6\u4e2a\u6570\u5171\u6709 \u4e2a\uff1b\u771f\u5b50\u96c6\u6709 \u20131\u4e2a\uff1b\u975e\u7a7a\u5b50\u96c6\u6709 \u20131\u4e2a\uff1b\u975e\u7a7a\u7684\u771f\u5b50\u96c6\u6709 \u20132\u4e2a.
6.\u4e8c\u6b21\u51fd\u6570\u7684\u89e3\u6790\u5f0f\u7684\u4e09\u79cd\u5f62\u5f0f
(1)\u4e00\u822c\u5f0f ;
(2)\u9876\u70b9\u5f0f ;
(3)\u96f6\u70b9\u5f0f .
7.\u89e3\u8fde\u4e0d\u7b49\u5f0f \u5e38\u6709\u4ee5\u4e0b\u8f6c\u5316\u5f62\u5f0f
.
8.\u65b9\u7a0b \u5728 \u4e0a\u6709\u4e14\u53ea\u6709\u4e00\u4e2a\u5b9e\u6839,\u4e0e \u4e0d\u7b49\u4ef7,\u524d\u8005\u662f\u540e\u8005\u7684\u4e00\u4e2a\u5fc5\u8981\u800c\u4e0d\u662f\u5145\u5206\u6761\u4ef6.\u7279\u522b\u5730, \u65b9\u7a0b \u6709\u4e14\u53ea\u6709\u4e00\u4e2a\u5b9e\u6839\u5728 \u5185,\u7b49\u4ef7\u4e8e ,\u6216 \u4e14 ,\u6216 \u4e14 .
9.\u95ed\u533a\u95f4\u4e0a\u7684\u4e8c\u6b21\u51fd\u6570\u7684\u6700\u503c
\u4e8c\u6b21\u51fd\u6570 \u5728\u95ed\u533a\u95f4 \u4e0a\u7684\u6700\u503c\u53ea\u80fd\u5728 \u5904\u53ca\u533a\u95f4\u7684\u4e24\u7aef\u70b9\u5904\u53d6\u5f97\uff0c\u5177\u4f53\u5982\u4e0b\uff1a
(1)\u5f53a>0\u65f6\uff0c\u82e5 \uff0c\u5219 \uff1b
\uff0c \uff0c .
(2)\u5f53a<0\u65f6\uff0c\u82e5 \uff0c\u5219 \uff0c\u82e5 \uff0c\u5219 \uff0c .
10.\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u5b9e\u6839\u5206\u5e03
\u4f9d\u636e\uff1a\u82e5 \uff0c\u5219\u65b9\u7a0b \u5728\u533a\u95f4 \u5185\u81f3\u5c11\u6709\u4e00\u4e2a\u5b9e\u6839 .
\u8bbe \uff0c\u5219
\uff081\uff09\u65b9\u7a0b \u5728\u533a\u95f4 \u5185\u6709\u6839\u7684\u5145\u8981\u6761\u4ef6\u4e3a \u6216 \uff1b
\uff082\uff09\u65b9\u7a0b \u5728\u533a\u95f4 \u5185\u6709\u6839\u7684\u5145\u8981\u6761\u4ef6\u4e3a \u6216 \u6216 \u6216 \uff1b
\uff083\uff09\u65b9\u7a0b \u5728\u533a\u95f4 \u5185\u6709\u6839\u7684\u5145\u8981\u6761\u4ef6\u4e3a \u6216 .
11.\u5b9a\u533a\u95f4\u4e0a\u542b\u53c2\u6570\u7684\u4e8c\u6b21\u4e0d\u7b49\u5f0f\u6052\u6210\u7acb\u7684\u6761\u4ef6\u4f9d\u636e
(1)\u5728\u7ed9\u5b9a\u533a\u95f4 \u7684\u5b50\u533a\u95f4 \uff08\u5f62\u5982 \uff0c \uff0c \u4e0d\u540c\uff09\u4e0a\u542b\u53c2\u6570\u7684\u4e8c\u6b21\u4e0d\u7b49\u5f0f ( \u4e3a\u53c2\u6570)\u6052\u6210\u7acb\u7684\u5145\u8981\u6761\u4ef6\u662f .
(2)\u5728\u7ed9\u5b9a\u533a\u95f4 \u7684\u5b50\u533a\u95f4\u4e0a\u542b\u53c2\u6570\u7684\u4e8c\u6b21\u4e0d\u7b49\u5f0f ( \u4e3a\u53c2\u6570)\u6052\u6210\u7acb\u7684\u5145\u8981\u6761\u4ef6\u662f .
(3) \u6052\u6210\u7acb\u7684\u5145\u8981\u6761\u4ef6\u662f \u6216 .
12.\u771f\u503c\u8868
pq\u975epp\u6216qp\u4e14q
\u771f\u771f\u5047\u771f\u771f
\u771f\u5047\u5047\u771f\u5047
\u5047\u771f\u771f\u771f\u5047
\u5047\u5047\u771f\u5047\u5047
13.\u5e38\u89c1\u7ed3\u8bba\u7684\u5426\u5b9a\u5f62\u5f0f
\u539f\u7ed3\u8bba\u53cd\u8bbe\u8bcd\u539f\u7ed3\u8bba\u53cd\u8bbe\u8bcd
\u662f\u4e0d\u662f\u81f3\u5c11\u6709\u4e00\u4e2a\u4e00\u4e2a\u4e5f\u6ca1\u6709
\u90fd\u662f\u4e0d\u90fd\u662f\u81f3\u591a\u6709\u4e00\u4e2a\u81f3\u5c11\u6709\u4e24\u4e2a
\u5927\u4e8e\u4e0d\u5927\u4e8e\u81f3\u5c11\u6709 \u4e2a
\u81f3\u591a\u6709\uff08 \uff09\u4e2a
\u5c0f\u4e8e\u4e0d\u5c0f\u4e8e\u81f3\u591a\u6709 \u4e2a
\u81f3\u5c11\u6709\uff08 \uff09\u4e2a
\u5bf9\u6240\u6709 \uff0c
\u6210\u7acb\u5b58\u5728\u67d0 \uff0c
\u4e0d\u6210\u7acb
\u6216
\u4e14
\u5bf9\u4efb\u4f55 \uff0c
\u4e0d\u6210\u7acb\u5b58\u5728\u67d0 \uff0c
\u6210\u7acb
\u4e14
\u6216
14.\u56db\u79cd\u547d\u9898\u7684\u76f8\u4e92\u5173\u7cfb
\u539f\u547d\u9898\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u4e92\u9006\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u9006\u547d\u9898
\u82e5p\u5219q\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u82e5q\u5219p
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u4e92\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u4e92
\u3000\u3000\u4e92\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u4e3a\u3000\u3000\u3000\u4e3a\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u4e92
\u3000\u3000\u5426\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u5426
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u9006\u3000\u3000\u3000\u9006\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000
\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u5426\u3000\u3000\u3000\u3000\u3000\u3000 \u5426
\u5426\u547d\u9898\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u9006\u5426\u547d\u9898\u3000\u3000\u3000
\u82e5\u975ep\u5219\u975eq\u3000\u3000\u3000\u3000\u4e92\u9006\u3000\u3000\u3000\u3000\u3000\u3000\u82e5\u975eq\u5219\u975ep
15.\u5145\u8981\u6761\u4ef6
\uff081\uff09\u5145\u5206\u6761\u4ef6\uff1a\u82e5 \uff0c\u5219 \u662f \u5145\u5206\u6761\u4ef6.
\uff082\uff09\u5fc5\u8981\u6761\u4ef6\uff1a\u82e5 \uff0c\u5219 \u662f \u5fc5\u8981\u6761\u4ef6.
\uff083\uff09\u5145\u8981\u6761\u4ef6\uff1a\u82e5 \uff0c\u4e14 \uff0c\u5219 \u662f \u5145\u8981\u6761\u4ef6.
\u6ce8\uff1a\u5982\u679c\u7532\u662f\u4e59\u7684\u5145\u5206\u6761\u4ef6\uff0c\u5219\u4e59\u662f\u7532\u7684\u5fc5\u8981\u6761\u4ef6\uff1b\u53cd\u4e4b\u4ea6\u7136.
16.\u51fd\u6570\u7684\u5355\u8c03\u6027
(1)\u8bbe \u90a3\u4e48
\u4e0a\u662f\u589e\u51fd\u6570\uff1b
\u4e0a\u662f\u51cf\u51fd\u6570.
(2)\u8bbe\u51fd\u6570 \u5728\u67d0\u4e2a\u533a\u95f4\u5185\u53ef\u5bfc\uff0c\u5982\u679c \uff0c\u5219 \u4e3a\u589e\u51fd\u6570\uff1b\u5982\u679c \uff0c\u5219 \u4e3a\u51cf\u51fd\u6570.
17.\u5982\u679c\u51fd\u6570 \u548c \u90fd\u662f\u51cf\u51fd\u6570,\u5219\u5728\u516c\u5171\u5b9a\u4e49\u57df\u5185,\u548c\u51fd\u6570 \u4e5f\u662f\u51cf\u51fd\u6570; \u5982\u679c\u51fd\u6570 \u548c \u5728\u5176\u5bf9\u5e94\u7684\u5b9a\u4e49\u57df\u4e0a\u90fd\u662f\u51cf\u51fd\u6570,\u5219\u590d\u5408\u51fd\u6570 \u662f\u589e\u51fd\u6570.
18\uff0e\u5947\u5076\u51fd\u6570\u7684\u56fe\u8c61\u7279\u5f81
\u5947\u51fd\u6570\u7684\u56fe\u8c61\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff0c\u5076\u51fd\u6570\u7684\u56fe\u8c61\u5173\u4e8ey\u8f74\u5bf9\u79f0;\u53cd\u8fc7\u6765\uff0c\u5982\u679c\u4e00\u4e2a\u51fd\u6570\u7684\u56fe\u8c61\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff0c\u90a3\u4e48\u8fd9\u4e2a\u51fd\u6570\u662f\u5947\u51fd\u6570\uff1b\u5982\u679c\u4e00\u4e2a\u51fd\u6570\u7684\u56fe\u8c61\u5173\u4e8ey\u8f74\u5bf9\u79f0\uff0c\u90a3\u4e48\u8fd9\u4e2a\u51fd\u6570\u662f\u5076\u51fd\u6570\uff0e
19.\u82e5\u51fd\u6570 \u662f\u5076\u51fd\u6570\uff0c\u5219 \uff1b\u82e5\u51fd\u6570 \u662f\u5076\u51fd\u6570\uff0c\u5219 .
20.\u5bf9\u4e8e\u51fd\u6570 ( ), \u6052\u6210\u7acb,\u5219\u51fd\u6570 \u7684\u5bf9\u79f0\u8f74\u662f\u51fd\u6570 ;\u4e24\u4e2a\u51fd\u6570 \u4e0e \u7684\u56fe\u8c61\u5173\u4e8e\u76f4\u7ebf \u5bf9\u79f0.
21.\u82e5 ,\u5219\u51fd\u6570 \u7684\u56fe\u8c61\u5173\u4e8e\u70b9 \u5bf9\u79f0; \u82e5 ,\u5219\u51fd\u6570 \u4e3a\u5468\u671f\u4e3a \u7684\u5468\u671f\u51fd\u6570.
22\uff0e\u591a\u9879\u5f0f\u51fd\u6570 \u7684\u5947\u5076\u6027
\u591a\u9879\u5f0f\u51fd\u6570 \u662f\u5947\u51fd\u6570 \u7684\u5076\u6b21\u9879(\u5373\u5947\u6570\u9879)\u7684\u7cfb\u6570\u5168\u4e3a\u96f6.
\u591a\u9879\u5f0f\u51fd\u6570 \u662f\u5076\u51fd\u6570 \u7684\u5947\u6b21\u9879(\u5373\u5076\u6570\u9879)\u7684\u7cfb\u6570\u5168\u4e3a\u96f6.
23.\u51fd\u6570 \u7684\u56fe\u8c61\u7684\u5bf9\u79f0\u6027
(1)\u51fd\u6570 \u7684\u56fe\u8c61\u5173\u4e8e\u76f4\u7ebf \u5bf9\u79f0
.
(2)\u51fd\u6570 \u7684\u56fe\u8c61\u5173\u4e8e\u76f4\u7ebf \u5bf9\u79f0
.
24.\u4e24\u4e2a\u51fd\u6570\u56fe\u8c61\u7684\u5bf9\u79f0\u6027
(1)\u51fd\u6570 \u4e0e\u51fd\u6570 \u7684\u56fe\u8c61\u5173\u4e8e\u76f4\u7ebf (\u5373 \u8f74)\u5bf9\u79f0.
(2)\u51fd\u6570 \u4e0e\u51fd\u6570 \u7684\u56fe\u8c61\u5173\u4e8e\u76f4\u7ebf \u5bf9\u79f0.
(3)\u51fd\u6570 \u548c \u7684\u56fe\u8c61\u5173\u4e8e\u76f4\u7ebfy=x\u5bf9\u79f0.
25.\u82e5\u5c06\u51fd\u6570 \u7684\u56fe\u8c61\u53f3\u79fb \u3001\u4e0a\u79fb \u4e2a\u5355\u4f4d\uff0c\u5f97\u5230\u51fd\u6570 \u7684\u56fe\u8c61\uff1b\u82e5\u5c06\u66f2\u7ebf \u7684\u56fe\u8c61\u53f3\u79fb \u3001\u4e0a\u79fb \u4e2a\u5355\u4f4d\uff0c\u5f97\u5230\u66f2\u7ebf \u7684\u56fe\u8c61.
26\uff0e\u4e92\u4e3a\u53cd\u51fd\u6570\u7684\u4e24\u4e2a\u51fd\u6570\u7684\u5173\u7cfb
.
27.\u82e5\u51fd\u6570 \u5b58\u5728\u53cd\u51fd\u6570,\u5219\u5176\u53cd\u51fd\u6570\u4e3a ,\u5e76\u4e0d\u662f ,\u800c\u51fd\u6570 \u662f \u7684\u53cd\u51fd\u6570.
28.\u51e0\u4e2a\u5e38\u89c1\u7684\u51fd\u6570\u65b9\u7a0b
(1)\u6b63\u6bd4\u4f8b\u51fd\u6570 , .
(2)\u6307\u6570\u51fd\u6570 , .
(3)\u5bf9\u6570\u51fd\u6570 , .
(4)\u5e42\u51fd\u6570 , .
(5)\u4f59\u5f26\u51fd\u6570 ,\u6b63\u5f26\u51fd\u6570 \uff0c \uff0c
.
29.\u51e0\u4e2a\u51fd\u6570\u65b9\u7a0b\u7684\u5468\u671f(\u7ea6\u5b9aa>0)
\uff081\uff09 \uff0c\u5219 \u7684\u5468\u671fT=a\uff1b
\uff082\uff09 \uff0c
\u6216 \uff0c
\u6216 ,
\u6216 ,\u5219 \u7684\u5468\u671fT=2a\uff1b
(3) \uff0c\u5219 \u7684\u5468\u671fT=3a\uff1b
(4) \u4e14 \uff0c\u5219 \u7684\u5468\u671fT=4a\uff1b
(5)
,\u5219 \u7684\u5468\u671fT=5a\uff1b
(6) \uff0c\u5219 \u7684\u5468\u671fT=6a.
30.\u5206\u6570\u6307\u6570\u5e42
(1) \uff08 \uff0c\u4e14 \uff09.
(2) \uff08 \uff0c\u4e14 \uff09.
31\uff0e\u6839\u5f0f\u7684\u6027\u8d28
\uff081\uff09 .
\uff082\uff09\u5f53 \u4e3a\u5947\u6570\u65f6\uff0c \uff1b
\u5f53 \u4e3a\u5076\u6570\u65f6\uff0c .
32\uff0e\u6709\u7406\u6307\u6570\u5e42\u7684\u8fd0\u7b97\u6027\u8d28
(1) .
(2) .
(3) .
\u6ce8\uff1a \u82e5a\uff1e0\uff0cp\u662f\u4e00\u4e2a\u65e0\u7406\u6570\uff0c\u5219ap\u8868\u793a\u4e00\u4e2a\u786e\u5b9a\u7684\u5b9e\u6570\uff0e\u4e0a\u8ff0\u6709\u7406\u6307\u6570\u5e42\u7684\u8fd0\u7b97\u6027\u8d28\uff0c\u5bf9\u4e8e\u65e0\u7406\u6570\u6307\u6570\u5e42\u90fd\u9002\u7528.
33.\u6307\u6570\u5f0f\u4e0e\u5bf9\u6570\u5f0f\u7684\u4e92\u5316\u5f0f
.
34.\u5bf9\u6570\u7684\u6362\u5e95\u516c\u5f0f
( ,\u4e14 , ,\u4e14 , ).
\u63a8\u8bba ( ,\u4e14 , ,\u4e14 , , ).
35\uff0e\u5bf9\u6570\u7684\u56db\u5219\u8fd0\u7b97\u6cd5\u5219
\u82e5a\uff1e0\uff0ca\u22601\uff0cM\uff1e0\uff0cN\uff1e0\uff0c\u5219
(1) ;
(2) ;
(3) .
36.\u8bbe\u51fd\u6570 ,\u8bb0 .\u82e5 \u7684\u5b9a\u4e49\u57df\u4e3a ,\u5219 \uff0c\u4e14 ;\u82e5 \u7684\u503c\u57df\u4e3a ,\u5219 \uff0c\u4e14 .\u5bf9\u4e8e \u7684\u60c5\u5f62,\u9700\u8981\u5355\u72ec\u68c0\u9a8c.
37. \u5bf9\u6570\u6362\u5e95\u4e0d\u7b49\u5f0f\u53ca\u5176\u63a8\u5e7f
\u82e5 , , , ,\u5219\u51fd\u6570
(1)\u5f53 \u65f6,\u5728 \u548c \u4e0a \u4e3a\u589e\u51fd\u6570.
\uff0c (2)\u5f53 \u65f6,\u5728 \u548c \u4e0a \u4e3a\u51cf\u51fd\u6570.
\u63a8\u8bba:\u8bbe \uff0c \uff0c \uff0c\u4e14 \uff0c\u5219
\uff081\uff09 .
\uff082\uff09 .
38. \u5e73\u5747\u589e\u957f\u7387\u7684\u95ee\u9898
\u5982\u679c\u539f\u6765\u4ea7\u503c\u7684\u57fa\u7840\u6570\u4e3aN\uff0c\u5e73\u5747\u589e\u957f\u7387\u4e3a \uff0c\u5219\u5bf9\u4e8e\u65f6\u95f4 \u7684\u603b\u4ea7\u503c \uff0c\u6709 .
39.\u6570\u5217\u7684\u540c\u9879\u516c\u5f0f\u4e0e\u524dn\u9879\u7684\u548c\u7684\u5173\u7cfb
( \u6570\u5217 \u7684\u524dn\u9879\u7684\u548c\u4e3a ).
40.\u7b49\u5dee\u6570\u5217\u7684\u901a\u9879\u516c\u5f0f
\uff1b
\u5176\u524dn\u9879\u548c\u516c\u5f0f\u4e3a
.
41.\u7b49\u6bd4\u6570\u5217\u7684\u901a\u9879\u516c\u5f0f
\uff1b
\u5176\u524dn\u9879\u7684\u548c\u516c\u5f0f\u4e3a
\u6216 .
42.\u7b49\u6bd4\u5dee\u6570\u5217 : \u7684\u901a\u9879\u516c\u5f0f\u4e3a
\uff1b
\u5176\u524dn\u9879\u548c\u516c\u5f0f\u4e3a
.
43.\u5206\u671f\u4ed8\u6b3e(\u6309\u63ed\u8d37\u6b3e)
\u6bcf\u6b21\u8fd8\u6b3e \u5143(\u8d37\u6b3e \u5143, \u6b21\u8fd8\u6e05,\u6bcf\u671f\u5229\u7387\u4e3a ).
44\uff0e\u5e38\u89c1\u4e09\u89d2\u4e0d\u7b49\u5f0f
\uff081\uff09\u82e5 \uff0c\u5219 .
(2) \u82e5 \uff0c\u5219 .
(3) .
45.\u540c\u89d2\u4e09\u89d2\u51fd\u6570\u7684\u57fa\u672c\u5173\u7cfb\u5f0f
\uff0c = \uff0c .
46.\u6b63\u5f26\u3001\u4f59\u5f26\u7684\u8bf1\u5bfc\u516c\u5f0f
47.\u548c\u89d2\u4e0e\u5dee\u89d2\u516c\u5f0f
;
;
.
(\u5e73\u65b9\u6b63\u5f26\u516c\u5f0f);
.
= (\u8f85\u52a9\u89d2 \u6240\u5728\u8c61\u9650\u7531\u70b9 \u7684\u8c61\u9650\u51b3\u5b9a, ).
48.\u4e8c\u500d\u89d2\u516c\u5f0f
.
.
.
49. \u4e09\u500d\u89d2\u516c\u5f0f
.
. .
50.\u4e09\u89d2\u51fd\u6570\u7684\u5468\u671f\u516c\u5f0f
\u51fd\u6570 \uff0cx\u2208R\u53ca\u51fd\u6570 \uff0cx\u2208R(A,\u03c9, \u4e3a\u5e38\u6570\uff0c\u4e14A\u22600\uff0c\u03c9\uff1e0)\u7684\u5468\u671f \uff1b\u51fd\u6570 \uff0c (A,\u03c9, \u4e3a\u5e38\u6570\uff0c\u4e14A\u22600\uff0c\u03c9\uff1e0)\u7684\u5468\u671f .
51.\u6b63\u5f26\u5b9a\u7406
.
52.\u4f59\u5f26\u5b9a\u7406
;
;
.
53.\u9762\u79ef\u5b9a\u7406
\uff081\uff09 \uff08 \u5206\u522b\u8868\u793aa\u3001b\u3001c\u8fb9\u4e0a\u7684\u9ad8\uff09.
\uff082\uff09 .
(3) .
54.\u4e09\u89d2\u5f62\u5185\u89d2\u548c\u5b9a\u7406
\u5728\u25b3ABC\u4e2d\uff0c\u6709
.
55. \u7b80\u5355\u7684\u4e09\u89d2\u65b9\u7a0b\u7684\u901a\u89e3
.
.
.
\u7279\u522b\u5730,\u6709
.
.
.
56.\u6700\u7b80\u5355\u7684\u4e09\u89d2\u4e0d\u7b49\u5f0f\u53ca\u5176\u89e3\u96c6
.
.
.
.
.
.
57.\u5b9e\u6570\u4e0e\u5411\u91cf\u7684\u79ef\u7684\u8fd0\u7b97\u5f8b
\u8bbe\u03bb\u3001\u03bc\u4e3a\u5b9e\u6570\uff0c\u90a3\u4e48
(1) \u7ed3\u5408\u5f8b\uff1a\u03bb(\u03bca)=(\u03bb\u03bc)a;
(2)\u7b2c\u4e00\u5206\u914d\u5f8b\uff1a(\u03bb+\u03bc)a=\u03bba+\u03bca;
(3)\u7b2c\u4e8c\u5206\u914d\u5f8b\uff1a\u03bb(a+b)=\u03bba+\u03bbb.
58.\u5411\u91cf\u7684\u6570\u91cf\u79ef\u7684\u8fd0\u7b97\u5f8b\uff1a
(1) a•b= b•a \uff08\u4ea4\u6362\u5f8b\uff09;
(2)\uff08 a\uff09•b= \uff08a•b\uff09= a•b= a•\uff08 b\uff09;
(3)\uff08a+b\uff09•c= a •c +b•c.
59.\u5e73\u9762\u5411\u91cf\u57fa\u672c\u5b9a\u7406
\u5982\u679ce1\u3001e 2\u662f\u540c\u4e00\u5e73\u9762\u5185\u7684\u4e24\u4e2a\u4e0d\u5171\u7ebf\u5411\u91cf\uff0c\u90a3\u4e48\u5bf9\u4e8e\u8fd9\u4e00\u5e73\u9762\u5185\u7684\u4efb\u4e00\u5411\u91cf\uff0c\u6709\u4e14\u53ea\u6709\u4e00\u5bf9\u5b9e\u6570\u03bb1\u3001\u03bb2\uff0c\u4f7f\u5f97a=\u03bb1e1+\u03bb2e2\uff0e
\u4e0d\u5171\u7ebf\u7684\u5411\u91cfe1\u3001e2\u53eb\u505a\u8868\u793a\u8fd9\u4e00\u5e73\u9762\u5185\u6240\u6709\u5411\u91cf\u7684\u4e00\u7ec4\u57fa\u5e95\uff0e
60\uff0e\u5411\u91cf\u5e73\u884c\u7684\u5750\u6807\u8868\u793a
\u8bbea= ,b= \uff0c\u4e14b 0\uff0c\u5219a b(b 0) .
53. a\u4e0eb\u7684\u6570\u91cf\u79ef(\u6216\u5185\u79ef)
a•b=|a||b|cos\u03b8\uff0e
61. a•b\u7684\u51e0\u4f55\u610f\u4e49
\u6570\u91cf\u79efa•b\u7b49\u4e8ea\u7684\u957f\u5ea6|a|\u4e0eb\u5728a\u7684\u65b9\u5411\u4e0a\u7684\u6295\u5f71|b|cos\u03b8\u7684\u4e58\u79ef\uff0e
62.\u5e73\u9762\u5411\u91cf\u7684\u5750\u6807\u8fd0\u7b97
(1)\u8bbea= ,b= \uff0c\u5219a+b= .
(2)\u8bbea= ,b= \uff0c\u5219a-b= .
(3)\u8bbeA \uff0cB ,\u5219 .
(4)\u8bbea= \uff0c\u5219 a= .
(5)\u8bbea= ,b= \uff0c\u5219a•b= .
63.\u4e24\u5411\u91cf\u7684\u5939\u89d2\u516c\u5f0f
(a= ,b= ).
64.\u5e73\u9762\u4e24\u70b9\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f
=
(A \uff0cB ).
65.\u5411\u91cf\u7684\u5e73\u884c\u4e0e\u5782\u76f4
\u8bbea= ,b= \uff0c\u4e14b 0\uff0c\u5219
A||b b=\u03bba .
a b(a 0) a•b=0 .
66.\u7ebf\u6bb5\u7684\u5b9a\u6bd4\u5206\u516c\u5f0f
\u8bbe \uff0c \uff0c \u662f\u7ebf\u6bb5 \u7684\u5206\u70b9, \u662f\u5b9e\u6570\uff0c\u4e14 \uff0c\u5219
\uff08 \uff09.
67.\u4e09\u89d2\u5f62\u7684\u91cd\u5fc3\u5750\u6807\u516c\u5f0f
\u25b3ABC\u4e09\u4e2a\u9876\u70b9\u7684\u5750\u6807\u5206\u522b\u4e3a \u3001 \u3001 ,\u5219\u25b3ABC\u7684\u91cd\u5fc3\u7684\u5750\u6807\u662f .
68.\u70b9\u7684\u5e73\u79fb\u516c\u5f0f
.
\u6ce8:\u56fe\u5f62F\u4e0a\u7684\u4efb\u610f\u4e00\u70b9P(x\uff0cy)\u5728\u5e73\u79fb\u540e\u56fe\u5f62 \u4e0a\u7684\u5bf9\u5e94\u70b9\u4e3a \uff0c\u4e14 \u7684\u5750\u6807\u4e3a .
69.\u201c\u6309\u5411\u91cf\u5e73\u79fb\u201d\u7684\u51e0\u4e2a\u7ed3\u8bba
\uff081\uff09\u70b9 \u6309\u5411\u91cfa= \u5e73\u79fb\u540e\u5f97\u5230\u70b9 .
(2) \u51fd\u6570 \u7684\u56fe\u8c61 \u6309\u5411\u91cfa= \u5e73\u79fb\u540e\u5f97\u5230\u56fe\u8c61 ,\u5219 \u7684\u51fd\u6570\u89e3\u6790\u5f0f\u4e3a .
(3) \u56fe\u8c61 \u6309\u5411\u91cfa= \u5e73\u79fb\u540e\u5f97\u5230\u56fe\u8c61 ,\u82e5 \u7684\u89e3\u6790\u5f0f ,\u5219 \u7684\u51fd\u6570\u89e3\u6790\u5f0f\u4e3a .
(4)\u66f2\u7ebf : \u6309\u5411\u91cfa= \u5e73\u79fb\u540e\u5f97\u5230\u56fe\u8c61 ,\u5219 \u7684\u65b9\u7a0b\u4e3a .
(5) \u5411\u91cfm= \u6309\u5411\u91cfa= \u5e73\u79fb\u540e\u5f97\u5230\u7684\u5411\u91cf\u4ecd\u7136\u4e3am= .
70. \u4e09\u89d2\u5f62\u4e94\u201c\u5fc3\u201d\u5411\u91cf\u5f62\u5f0f\u7684\u5145\u8981\u6761\u4ef6
\u8bbe \u4e3a \u6240\u5728\u5e73\u9762\u4e0a\u4e00\u70b9\uff0c\u89d2 \u6240\u5bf9\u8fb9\u957f\u5206\u522b\u4e3a \uff0c\u5219
\uff081\uff09 \u4e3a \u7684\u5916\u5fc3 .
\uff082\uff09 \u4e3a \u7684\u91cd\u5fc3 .
\uff083\uff09 \u4e3a \u7684\u5782\u5fc3 .
\uff084\uff09 \u4e3a \u7684\u5185\u5fc3 .
\uff085\uff09 \u4e3a \u7684 \u7684\u65c1\u5fc3 .
71.\u5e38\u7528\u4e0d\u7b49\u5f0f\uff1a
\uff081\uff09 (\u5f53\u4e14\u4ec5\u5f53a\uff1db\u65f6\u53d6\u201c=\u201d\u53f7)\uff0e
\uff082\uff09 (\u5f53\u4e14\u4ec5\u5f53a\uff1db\u65f6\u53d6\u201c=\u201d\u53f7)\uff0e
\uff083\uff09
\uff084\uff09\u67ef\u897f\u4e0d\u7b49\u5f0f
\uff085\uff09 .
72.\u6781\u503c\u5b9a\u7406
\u5df2\u77e5 \u90fd\u662f\u6b63\u6570\uff0c\u5219\u6709
\uff081\uff09\u82e5\u79ef \u662f\u5b9a\u503c \uff0c\u5219\u5f53 \u65f6\u548c \u6709\u6700\u5c0f\u503c \uff1b
\uff082\uff09\u82e5\u548c \u662f\u5b9a\u503c \uff0c\u5219\u5f53 \u65f6\u79ef \u6709\u6700\u5927\u503c .
\u63a8\u5e7f \u5df2\u77e5 \uff0c\u5219\u6709
\uff081\uff09\u82e5\u79ef \u662f\u5b9a\u503c,\u5219\u5f53 \u6700\u5927\u65f6, \u6700\u5927\uff1b
\u5f53 \u6700\u5c0f\u65f6, \u6700\u5c0f.
\uff082\uff09\u82e5\u548c \u662f\u5b9a\u503c,\u5219\u5f53 \u6700\u5927\u65f6, \u6700\u5c0f\uff1b
\u5f53 \u6700\u5c0f\u65f6, \u6700\u5927.
73.\u4e00\u5143\u4e8c\u6b21\u4e0d\u7b49\u5f0f \uff0c\u5982\u679c \u4e0e \u540c\u53f7\uff0c\u5219\u5176\u89e3\u96c6\u5728\u4e24\u6839\u4e4b\u5916\uff1b\u5982\u679c \u4e0e \u5f02\u53f7\uff0c\u5219\u5176\u89e3\u96c6\u5728\u4e24\u6839\u4e4b\u95f4.\u7b80\u8a00\u4e4b\uff1a\u540c\u53f7\u4e24\u6839\u4e4b\u5916\uff0c\u5f02\u53f7\u4e24\u6839\u4e4b\u95f4.
\uff1b
.
74.\u542b\u6709\u7edd\u5bf9\u503c\u7684\u4e0d\u7b49\u5f0f
\u5f53a> 0\u65f6\uff0c\u6709
.
\u6216 .
75.\u65e0\u7406\u4e0d\u7b49\u5f0f
\uff081\uff09 .
\uff082\uff09 .
\uff083\uff09 .
76.\u6307\u6570\u4e0d\u7b49\u5f0f\u4e0e\u5bf9\u6570\u4e0d\u7b49\u5f0f
(1)\u5f53 \u65f6,
;
.
(2)\u5f53 \u65f6,
;
77.\u659c\u7387\u516c\u5f0f
\uff08 \u3001 \uff09.
78.\u76f4\u7ebf\u7684\u4e94\u79cd\u65b9\u7a0b
\uff081\uff09\u70b9\u659c\u5f0f (\u76f4\u7ebf \u8fc7\u70b9 \uff0c\u4e14\u659c\u7387\u4e3a )\uff0e
\uff082\uff09\u659c\u622a\u5f0f (b\u4e3a\u76f4\u7ebf \u5728y\u8f74\u4e0a\u7684\u622a\u8ddd).
\uff083\uff09\u4e24\u70b9\u5f0f ( )( \u3001 ( )).
(4)\u622a\u8ddd\u5f0f ( \u5206\u522b\u4e3a\u76f4\u7ebf\u7684\u6a2a\u3001\u7eb5\u622a\u8ddd\uff0c )
\uff085\uff09\u4e00\u822c\u5f0f (\u5176\u4e2dA\u3001B\u4e0d\u540c\u65f6\u4e3a0).
79.\u4e24\u6761\u76f4\u7ebf\u7684\u5e73\u884c\u548c\u5782\u76f4
(1)\u82e5 \uff0c
\u2460 ;
\u2461 .
(2)\u82e5 , ,\u4e14A1\u3001A2\u3001B1\u3001B2\u90fd\u4e0d\u4e3a\u96f6,
\u2460 \uff1b
\u2461 \uff1b
80.\u5939\u89d2\u516c\u5f0f
(1) .
( \uff0c , )
(2) .
( , , ).
\u76f4\u7ebf \u65f6\uff0c\u76f4\u7ebfl1\u4e0el2\u7684\u5939\u89d2\u662f .
81. \u5230 \u7684\u89d2\u516c\u5f0f
(1) .
( \uff0c , )
(2) .
( , , ).
\u76f4\u7ebf \u65f6\uff0c\u76f4\u7ebfl1\u5230l2\u7684\u89d2\u662f .
82\uff0e\u56db\u79cd\u5e38\u7528\u76f4\u7ebf\u7cfb\u65b9\u7a0b
(1)\u5b9a\u70b9\u76f4\u7ebf\u7cfb\u65b9\u7a0b\uff1a\u7ecf\u8fc7\u5b9a\u70b9 \u7684\u76f4\u7ebf\u7cfb\u65b9\u7a0b\u4e3a (\u9664\u76f4\u7ebf ),\u5176\u4e2d \u662f\u5f85\u5b9a\u7684\u7cfb\u6570; \u7ecf\u8fc7\u5b9a\u70b9 \u7684\u76f4\u7ebf\u7cfb\u65b9\u7a0b\u4e3a ,\u5176\u4e2d \u662f\u5f85\u5b9a\u7684\u7cfb\u6570\uff0e
(2)\u5171\u70b9\u76f4\u7ebf\u7cfb\u65b9\u7a0b\uff1a\u7ecf\u8fc7\u4e24\u76f4\u7ebf , \u7684\u4ea4\u70b9\u7684\u76f4\u7ebf\u7cfb\u65b9\u7a0b\u4e3a (\u9664 )\uff0c\u5176\u4e2d\u03bb\u662f\u5f85\u5b9a\u7684\u7cfb\u6570\uff0e
(3)\u5e73\u884c\u76f4\u7ebf\u7cfb\u65b9\u7a0b\uff1a\u76f4\u7ebf \u4e2d\u5f53\u659c\u7387k\u4e00\u5b9a\u800cb\u53d8\u52a8\u65f6\uff0c\u8868\u793a\u5e73\u884c\u76f4\u7ebf\u7cfb\u65b9\u7a0b\uff0e\u4e0e\u76f4\u7ebf \u5e73\u884c\u7684\u76f4\u7ebf\u7cfb\u65b9\u7a0b\u662f ( )\uff0c\u03bb\u662f\u53c2\u53d8\u91cf\uff0e
(4)\u5782\u76f4\u76f4\u7ebf\u7cfb\u65b9\u7a0b\uff1a\u4e0e\u76f4\u7ebf (A\u22600\uff0cB\u22600)\u5782\u76f4\u7684\u76f4\u7ebf\u7cfb\u65b9\u7a0b\u662f ,\u03bb\u662f\u53c2\u53d8\u91cf\uff0e
83.\u70b9\u5230\u76f4\u7ebf\u7684\u8ddd\u79bb
(\u70b9 ,\u76f4\u7ebf \uff1a ).
84. \u6216 \u6240\u8868\u793a\u7684\u5e73\u9762\u533a\u57df
\u8bbe\u76f4\u7ebf \uff0c\u5219 \u6216 \u6240\u8868\u793a\u7684\u5e73\u9762\u533a\u57df\u662f\uff1a
\u82e5 \uff0c\u5f53 \u4e0e \u540c\u53f7\u65f6\uff0c\u8868\u793a\u76f4\u7ebf \u7684\u4e0a\u65b9\u7684\u533a\u57df\uff1b\u5f53 \u4e0e \u5f02\u53f7\u65f6\uff0c\u8868\u793a\u76f4\u7ebf \u7684\u4e0b\u65b9\u7684\u533a\u57df.\u7b80\u8a00\u4e4b,\u540c\u53f7\u5728\u4e0a,\u5f02\u53f7\u5728\u4e0b.
\u82e5 \uff0c\u5f53 \u4e0e \u540c\u53f7\u65f6\uff0c\u8868\u793a\u76f4\u7ebf \u7684\u53f3\u65b9\u7684\u533a\u57df\uff1b\u5f53 \u4e0e \u5f02\u53f7\u65f6\uff0c\u8868\u793a\u76f4\u7ebf \u7684\u5de6\u65b9\u7684\u533a\u57df. \u7b80\u8a00\u4e4b,\u540c\u53f7\u5728\u53f3,\u5f02\u53f7\u5728\u5de6.
85. \u6216 \u6240\u8868\u793a\u7684\u5e73\u9762\u533a\u57df
\u8bbe\u66f2\u7ebf \uff08 \uff09\uff0c\u5219
\u6216 \u6240\u8868\u793a\u7684\u5e73\u9762\u533a\u57df\u662f\uff1a
\u6240\u8868\u793a\u7684\u5e73\u9762\u533a\u57df\u4e0a\u4e0b\u4e24\u90e8\u5206\uff1b
\u6240\u8868\u793a\u7684\u5e73\u9762\u533a\u57df\u4e0a\u4e0b\u4e24\u90e8\u5206.
86. \u5706\u7684\u56db\u79cd\u65b9\u7a0b
\uff081\uff09\u5706\u7684\u6807\u51c6\u65b9\u7a0b .
\uff082\uff09\u5706\u7684\u4e00\u822c\u65b9\u7a0b ( \uff1e0).
\uff083\uff09\u5706\u7684\u53c2\u6570\u65b9\u7a0b .
\uff084\uff09\u5706\u7684\u76f4\u5f84\u5f0f\u65b9\u7a0b (\u5706\u7684\u76f4\u5f84\u7684\u7aef\u70b9\u662f \u3001 ).
87. \u5706\u7cfb\u65b9\u7a0b
(1)\u8fc7\u70b9 , \u7684\u5706\u7cfb\u65b9\u7a0b\u662f
,\u5176\u4e2d \u662f\u76f4\u7ebf \u7684\u65b9\u7a0b,\u03bb\u662f\u5f85\u5b9a\u7684\u7cfb\u6570\uff0e
(2)\u8fc7\u76f4\u7ebf : \u4e0e\u5706 : \u7684\u4ea4\u70b9\u7684\u5706\u7cfb\u65b9\u7a0b\u662f ,\u03bb\u662f\u5f85\u5b9a\u7684\u7cfb\u6570\uff0e
(3) \u8fc7\u5706 : \u4e0e\u5706 : \u7684\u4ea4\u70b9\u7684\u5706\u7cfb\u65b9\u7a0b\u662f ,\u03bb\u662f\u5f85\u5b9a\u7684\u7cfb\u6570\uff0e
88.\u70b9\u4e0e\u5706\u7684\u4f4d\u7f6e\u5173\u7cfb
\u70b9 \u4e0e\u5706 \u7684\u4f4d\u7f6e\u5173\u7cfb\u6709\u4e09\u79cd
\u82e5 \uff0c\u5219
\u70b9 \u5728\u5706\u5916; \u70b9 \u5728\u5706\u4e0a; \u70b9 \u5728\u5706\u5185.
89.\u76f4\u7ebf\u4e0e\u5706\u7684\u4f4d\u7f6e\u5173\u7cfb
\u76f4\u7ebf \u4e0e\u5706 \u7684\u4f4d\u7f6e\u5173\u7cfb\u6709\u4e09\u79cd:
;
;
.
\u5176\u4e2d .
90.\u4e24\u5706\u4f4d\u7f6e\u5173\u7cfb\u7684\u5224\u5b9a\u65b9\u6cd5
\u8bbe\u4e24\u5706\u5706\u5fc3\u5206\u522b\u4e3aO1\uff0cO2\uff0c\u534a\u5f84\u5206\u522b\u4e3ar1\uff0cr2\uff0c
;
;
;
;
.
91.\u5706\u7684\u5207\u7ebf\u65b9\u7a0b
(1)\u5df2\u77e5\u5706 \uff0e
\u2460\u82e5\u5df2\u77e5\u5207\u70b9 \u5728\u5706\u4e0a\uff0c\u5219\u5207\u7ebf\u53ea\u6709\u4e00\u6761\uff0c\u5176\u65b9\u7a0b\u662f
.
\u5f53 \u5706\u5916\u65f6, \u8868\u793a\u8fc7\u4e24\u4e2a\u5207\u70b9\u7684\u5207\u70b9\u5f26\u65b9\u7a0b\uff0e
\u2461\u8fc7\u5706\u5916\u4e00\u70b9\u7684\u5207\u7ebf\u65b9\u7a0b\u53ef\u8bbe\u4e3a \uff0c\u518d\u5229\u7528\u76f8\u5207\u6761\u4ef6\u6c42k\uff0c\u8fd9\u65f6\u5fc5\u6709\u4e24\u6761\u5207\u7ebf\uff0c\u6ce8\u610f\u4e0d\u8981\u6f0f\u6389\u5e73\u884c\u4e8ey\u8f74\u7684\u5207\u7ebf\uff0e
\u2462\u659c\u7387\u4e3ak\u7684\u5207\u7ebf\u65b9\u7a0b\u53ef\u8bbe\u4e3a \uff0c\u518d\u5229\u7528\u76f8\u5207\u6761\u4ef6\u6c42b\uff0c\u5fc5\u6709\u4e24\u6761\u5207\u7ebf\uff0e
(2)\u5df2\u77e5\u5706 \uff0e
\u2460\u8fc7\u5706\u4e0a\u7684 \u70b9\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3a ;
\u2461\u659c\u7387\u4e3a \u7684\u5706\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3a .
92.\u692d\u5706 \u7684\u53c2\u6570\u65b9\u7a0b\u662f .
93.\u692d\u5706 \u7126\u534a\u5f84\u516c\u5f0f
\uff0c .
94\uff0e\u692d\u5706\u7684\u7684\u5185\u5916\u90e8
\uff081\uff09\u70b9 \u5728\u692d\u5706 \u7684\u5185\u90e8 .
\uff082\uff09\u70b9 \u5728\u692d\u5706 \u7684\u5916\u90e8 .
95. \u692d\u5706\u7684\u5207\u7ebf\u65b9\u7a0b
(1)\u692d\u5706 \u4e0a\u4e00\u70b9 \u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u662f .
\uff082\uff09\u8fc7\u692d\u5706 \u5916\u4e00\u70b9 \u6240\u5f15\u4e24\u6761\u5207\u7ebf\u7684\u5207\u70b9\u5f26\u65b9\u7a0b\u662f
.
\uff083\uff09\u692d\u5706 \u4e0e\u76f4\u7ebf \u76f8\u5207\u7684\u6761\u4ef6\u662f .
96.\u53cc\u66f2\u7ebf \u7684\u7126\u534a\u5f84\u516c\u5f0f
\uff0c .
97.\u53cc\u66f2\u7ebf\u7684\u5185\u5916\u90e8
(1)\u70b9 \u5728\u53cc\u66f2\u7ebf \u7684\u5185\u90e8 .
(2)\u70b9 \u5728\u53cc\u66f2\u7ebf \u7684\u5916\u90e8 .
98.\u53cc\u66f2\u7ebf\u7684\u65b9\u7a0b\u4e0e\u6e10\u8fd1\u7ebf\u65b9\u7a0b\u7684\u5173\u7cfb
(1\uff09\u82e5\u53cc\u66f2\u7ebf\u65b9\u7a0b\u4e3a \u6e10\u8fd1\u7ebf\u65b9\u7a0b\uff1a .
(2)\u82e5\u6e10\u8fd1\u7ebf\u65b9\u7a0b\u4e3a \u53cc\u66f2\u7ebf\u53ef\u8bbe\u4e3a .
(3)\u82e5\u53cc\u66f2\u7ebf\u4e0e \u6709\u516c\u5171\u6e10\u8fd1\u7ebf\uff0c\u53ef\u8bbe\u4e3a \uff08 \uff0c\u7126\u70b9\u5728x\u8f74\u4e0a\uff0c \uff0c\u7126\u70b9\u5728y\u8f74\u4e0a\uff09.
99. \u53cc\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b
(1)\u53cc\u66f2\u7ebf \u4e0a\u4e00\u70b9 \u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u662f .
\uff082\uff09\u8fc7\u53cc\u66f2\u7ebf \u5916\u4e00\u70b9 \u6240\u5f15\u4e24\u6761\u5207\u7ebf\u7684\u5207\u70b9\u5f26\u65b9\u7a0b\u662f
.
\uff083\uff09\u53cc\u66f2\u7ebf \u4e0e\u76f4\u7ebf \u76f8\u5207\u7684\u6761\u4ef6\u662f .
100. \u629b\u7269\u7ebf \u7684\u7126\u534a\u5f84\u516c\u5f0f
\u629b\u7269\u7ebf \u7126\u534a\u5f84 .
\u8fc7\u7126\u70b9\u5f26\u957f .
101.\u629b\u7269\u7ebf \u4e0a\u7684\u52a8\u70b9\u53ef\u8bbe\u4e3aP \u6216 P \uff0c\u5176\u4e2d .
102.\u4e8c\u6b21\u51fd\u6570 \u7684\u56fe\u8c61\u662f\u629b\u7269\u7ebf\uff1a\uff081\uff09\u9876\u70b9\u5750\u6807\u4e3a \uff1b\uff082\uff09\u7126\u70b9\u7684\u5750\u6807\u4e3a \uff1b\uff083\uff09\u51c6\u7ebf\u65b9\u7a0b\u662f .
103.\u629b\u7269\u7ebf\u7684\u5185\u5916\u90e8
(1)\u70b9 \u5728\u629b\u7269\u7ebf \u7684\u5185\u90e8 .
\u70b9 \u5728\u629b\u7269\u7ebf \u7684\u5916\u90e8 .
(2)\u70b9 \u5728\u629b\u7269\u7ebf \u7684\u5185\u90e8 .
\u70b9 \u5728\u629b\u7269\u7ebf \u7684\u5916\u90e8 .
(3)\u70b9 \u5728\u629b\u7269\u7ebf \u7684\u5185\u90e8 .
\u70b9 \u5728\u629b\u7269\u7ebf \u7684\u5916\u90e8 .
(4) \u70b9 \u5728\u629b\u7269\u7ebf \u7684\u5185\u90e8 .
\u70b9 \u5728\u629b\u7269\u7ebf \u7684\u5916\u90e8 .
104. \u629b\u7269\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b
(1)\u629b\u7269\u7ebf \u4e0a\u4e00\u70b9 \u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u662f .
\uff082\uff09\u8fc7\u629b\u7269\u7ebf \u5916\u4e00\u70b9 \u6240\u5f15\u4e24\u6761\u5207\u7ebf\u7684\u5207\u70b9\u5f26\u65b9\u7a0b\u662f .
\uff083\uff09\u629b\u7269\u7ebf \u4e0e\u76f4\u7ebf \u76f8\u5207\u7684\u6761\u4ef6\u662f .
105.\u4e24\u4e2a\u5e38\u89c1\u7684\u66f2\u7ebf\u7cfb\u65b9\u7a0b
(1)\u8fc7\u66f2\u7ebf , \u7684\u4ea4\u70b9\u7684\u66f2\u7ebf\u7cfb\u65b9\u7a0b\u662f
( \u4e3a\u53c2\u6570).
(2)\u5171\u7126\u70b9\u7684\u6709\u5fc3\u5706\u9525\u66f2\u7ebf\u7cfb\u65b9\u7a0b ,\u5176\u4e2d .\u5f53 \u65f6,\u8868\u793a\u692d\u5706; \u5f53 \u65f6,\u8868\u793a\u53cc\u66f2\u7ebf.
106.\u76f4\u7ebf\u4e0e\u5706\u9525\u66f2\u7ebf\u76f8\u4ea4\u7684\u5f26\u957f\u516c\u5f0f \u6216
\uff08\u5f26\u7aef\u70b9A \uff0c\u7531\u65b9\u7a0b \u6d88\u53bby\u5f97\u5230 \uff0c , \u4e3a\u76f4\u7ebf \u7684\u503e\u659c\u89d2\uff0c \u4e3a\u76f4\u7ebf\u7684\u659c\u7387\uff09.
107.\u5706\u9525\u66f2\u7ebf\u7684\u4e24\u7c7b\u5bf9\u79f0\u95ee\u9898
\uff081\uff09\u66f2\u7ebf \u5173\u4e8e\u70b9 \u6210\u4e2d\u5fc3\u5bf9\u79f0\u7684\u66f2\u7ebf\u662f .
\uff082\uff09\u66f2\u7ebf \u5173\u4e8e\u76f4\u7ebf \u6210\u8f74\u5bf9\u79f0\u7684\u66f2\u7ebf\u662f
.
108.\u201c\u56db\u7ebf\u201d\u4e00\u65b9\u7a0b
\u5bf9\u4e8e\u4e00\u822c\u7684\u4e8c\u6b21\u66f2\u7ebf \uff0c\u7528 \u4ee3 \uff0c\u7528 \u4ee3 \uff0c\u7528 \u4ee3 \uff0c\u7528 \u4ee3 \uff0c\u7528 \u4ee3 \u5373\u5f97\u65b9\u7a0b
\uff0c\u66f2\u7ebf\u7684\u5207\u7ebf\uff0c\u5207\u70b9\u5f26\uff0c\u4e2d\u70b9\u5f26\uff0c\u5f26\u4e2d\u70b9\u65b9\u7a0b\u5747\u662f\u6b64\u65b9\u7a0b\u5f97\u5230.
109\uff0e\u8bc1\u660e\u76f4\u7ebf\u4e0e\u76f4\u7ebf\u7684\u5e73\u884c\u7684\u601d\u8003\u9014\u5f84
\uff081\uff09\u8f6c\u5316\u4e3a\u5224\u5b9a\u5171\u9762\u4e8c\u76f4\u7ebf\u65e0\u4ea4\u70b9\uff1b
\uff082\uff09\u8f6c\u5316\u4e3a\u4e8c\u76f4\u7ebf\u540c\u4e0e\u7b2c\u4e09\u6761\u76f4\u7ebf\u5e73\u884c\uff1b
\uff083\uff09\u8f6c\u5316\u4e3a\u7ebf\u9762\u5e73\u884c\uff1b
\uff084\uff09\u8f6c\u5316\u4e3a\u7ebf\u9762\u5782\u76f4\uff1b
\uff085\uff09\u8f6c\u5316\u4e3a\u9762\u9762\u5e73\u884c.
110\uff0e\u8bc1\u660e\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5e73\u884c\u7684\u601d\u8003\u9014\u5f84
\uff081\uff09\u8f6c\u5316\u4e3a\u76f4\u7ebf\u4e0e\u5e73\u9762\u65e0\u516c\u5171\u70b9\uff1b
\uff082\uff09\u8f6c\u5316\u4e3a\u7ebf\u7ebf\u5e73\u884c\uff1b
\uff083\uff09\u8f6c\u5316\u4e3a\u9762\u9762\u5e73\u884c.
111\uff0e\u8bc1\u660e\u5e73\u9762\u4e0e\u5e73\u9762\u5e73\u884c\u7684\u601d\u8003\u9014\u5f84
\uff081\uff09\u8f6c\u5316\u4e3a\u5224\u5b9a\u4e8c\u5e73\u9762\u65e0\u516c\u5171\u70b9\uff1b
\uff082\uff09\u8f6c\u5316\u4e3a\u7ebf\u9762\u5e73\u884c\uff1b
\uff083\uff09\u8f6c\u5316\u4e3a\u7ebf\u9762\u5782\u76f4.
112\uff0e\u8bc1\u660e\u76f4\u7ebf\u4e0e\u76f4\u7ebf\u7684\u5782\u76f4\u7684\u601d\u8003\u9014\u5f84
\uff081\uff09\u8f6c\u5316\u4e3a\u76f8\u4ea4\u5782\u76f4\uff1b
\uff082\uff09\u8f6c\u5316\u4e3a\u7ebf\u9762\u5782\u76f4\uff1b
\uff083\uff09\u8f6c\u5316\u4e3a\u7ebf\u4e0e\u53e6\u4e00\u7ebf\u7684\u5c04\u5f71\u5782\u76f4\uff1b
\uff084\uff09\u8f6c\u5316\u4e3a\u7ebf\u4e0e\u5f62\u6210\u5c04\u5f71\u7684\u659c\u7ebf\u5782\u76f4.
113\uff0e\u8bc1\u660e\u76f4\u7ebf\u4e0e\u5e73\u9762\u5782\u76f4\u7684\u601d\u8003\u9014\u5f84
\uff081\uff09\u8f6c\u5316\u4e3a\u8be5\u76f4\u7ebf\u4e0e\u5e73\u9762\u5185\u4efb\u4e00\u76f4\u7ebf\u5782\u76f4\uff1b
\uff082\uff09\u8f6c\u5316\u4e3a\u8be5\u76f4\u7ebf\u4e0e\u5e73\u9762\u5185\u76f8\u4ea4\u4e8c\u76f4\u7ebf\u5782\u76f4\uff1b
\uff083\uff09\u8f6c\u5316\u4e3a\u8be5\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u4e00\u6761\u5782\u7ebf\u5e73\u884c\uff1b
\uff084\uff09\u8f6c\u5316\u4e3a\u8be5\u76f4\u7ebf\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5e73\u884c\u5e73\u9762\uff1b
\uff085\uff09\u8f6c\u5316\u4e3a\u8be5\u76f4\u7ebf\u4e0e\u4e24\u4e2a\u5782\u76f4\u5e73\u9762\u7684\u4ea4\u7ebf\u5782\u76f4.
114\uff0e\u8bc1\u660e\u5e73\u9762\u4e0e\u5e73\u9762\u7684\u5782\u76f4\u7684\u601d\u8003\u9014\u5f84
\uff081\uff09\u8f6c\u5316\u4e3a\u5224\u65ad\u4e8c\u9762\u89d2\u662f\u76f4\u4e8c\u9762\u89d2\uff1b
\uff082\uff09\u8f6c\u5316\u4e3a\u7ebf\u9762\u5782\u76f4.
115.\u7a7a\u95f4\u5411\u91cf\u7684\u52a0\u6cd5\u4e0e\u6570\u4e58\u5411\u91cf\u8fd0\u7b97\u7684\u8fd0\u7b97\u5f8b
(1)\u52a0\u6cd5\u4ea4\u6362\u5f8b\uff1aa\uff0bb=b\uff0ba\uff0e
(2)\u52a0\u6cd5\u7ed3\u5408\u5f8b\uff1a(a\uff0bb)\uff0bc=a\uff0b(b\uff0bc)\uff0e
(3)\u6570\u4e58\u5206\u914d\u5f8b\uff1a\u03bb(a\uff0bb)=\u03bba\uff0b\u03bbb\uff0e
116.\u5e73\u9762\u5411\u91cf\u52a0\u6cd5\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u6cd5\u5219\u5411\u7a7a\u95f4\u7684\u63a8\u5e7f
\u59cb\u70b9\u76f8\u540c\u4e14\u4e0d\u5728\u540c\u4e00\u4e2a\u5e73\u9762\u5185\u7684\u4e09\u4e2a\u5411\u91cf\u4e4b\u548c\uff0c\u7b49\u4e8e\u4ee5\u8fd9\u4e09\u4e2a\u5411\u91cf\u4e3a\u68f1\u7684\u5e73\u884c\u516d\u9762\u4f53\u7684\u4ee5\u516c\u5171\u59cb\u70b9\u4e3a\u59cb\u70b9\u7684\u5bf9\u89d2\u7ebf\u6240\u8868\u793a\u7684\u5411\u91cf.
117.\u5171\u7ebf\u5411\u91cf\u5b9a\u7406
\u5bf9\u7a7a\u95f4\u4efb\u610f\u4e24\u4e2a\u5411\u91cfa\u3001b(b\u22600 )\uff0ca\u2225b \u5b58\u5728\u5b9e\u6570\u03bb\u4f7fa=\u03bbb\uff0e
\u4e09\u70b9\u5171\u7ebf .
\u3001 \u5171\u7ebf\u4e14 \u4e0d\u5171\u7ebf \u4e14 \u4e0d\u5171\u7ebf.
118.\u5171\u9762\u5411\u91cf\u5b9a\u7406
\u5411\u91cfp\u4e0e\u4e24\u4e2a\u4e0d\u5171\u7ebf\u7684\u5411\u91cfa\u3001b\u5171\u9762\u7684 \u5b58\u5728\u5b9e\u6570\u5bf9 ,\u4f7f \uff0e
\u63a8\u8bba \u7a7a\u95f4\u4e00\u70b9P\u4f4d\u4e8e\u5e73\u9762MAB\u5185\u7684 \u5b58\u5728\u6709\u5e8f\u5b9e\u6570\u5bf9 ,\u4f7f \uff0c
\u6216\u5bf9\u7a7a\u95f4\u4efb\u4e00\u5b9a\u70b9O\uff0c\u6709\u5e8f\u5b9e\u6570\u5bf9 \uff0c\u4f7f .
119.\u5bf9\u7a7a\u95f4\u4efb\u4e00\u70b9 \u548c\u4e0d\u5171\u7ebf\u7684\u4e09\u70b9A\u3001B\u3001C\uff0c\u6ee1\u8db3 \uff08 \uff09\uff0c\u5219\u5f53 \u65f6\uff0c\u5bf9\u4e8e\u7a7a\u95f4\u4efb\u4e00\u70b9 \uff0c\u603b\u6709P\u3001A\u3001B\u3001C\u56db\u70b9\u5171\u9762\uff1b\u5f53 \u65f6\uff0c\u82e5 \u5e73\u9762ABC\uff0c\u5219P\u3001A\u3001B\u3001C\u56db\u70b9\u5171\u9762\uff1b\u82e5 \u5e73\u9762ABC\uff0c\u5219P\u3001A\u3001B\u3001C\u56db\u70b9\u4e0d\u5171\u9762\uff0e
\u56db\u70b9\u5171\u9762 \u4e0e \u3001 \u5171\u9762
\uff08 \u5e73\u9762ABC\uff09.
120.\u7a7a\u95f4\u5411\u91cf\u57fa\u672c\u5b9a\u7406
\u5982\u679c\u4e09\u4e2a\u5411\u91cfa\u3001b\u3001c\u4e0d\u5171\u9762\uff0c\u90a3\u4e48\u5bf9\u7a7a\u95f4\u4efb\u4e00\u5411\u91cfp\uff0c\u5b58\u5728\u4e00\u4e2a\u552f\u4e00\u7684\u6709\u5e8f\u5b9e\u6570\u7ec4x\uff0cy\uff0cz\uff0c\u4f7fp\uff1dxa\uff0byb\uff0bzc\uff0e
\u63a8\u8bba \u8bbeO\u3001A\u3001B\u3001C\u662f\u4e0d\u5171\u9762\u7684\u56db\u70b9\uff0c\u5219\u5bf9\u7a7a\u95f4\u4efb\u4e00\u70b9P\uff0c\u90fd\u5b58\u5728\u552f\u4e00\u7684\u4e09\u4e2a\u6709\u5e8f\u5b9e\u6570x\uff0cy\uff0cz\uff0c\u4f7f .
121.\u5c04\u5f71\u516c\u5f0f
\u5df2\u77e5\u5411\u91cf =a\u548c\u8f74 \uff0ce\u662f \u4e0a\u4e0e \u540c\u65b9\u5411\u7684\u5355\u4f4d\u5411\u91cf.\u4f5cA\u70b9\u5728 \u4e0a\u7684\u5c04\u5f71 \uff0c\u4f5cB\u70b9\u5728 \u4e0a\u7684\u5c04\u5f71 \uff0c\u5219
\u3008a\uff0ce\u3009=a•e
122.\u5411\u91cf\u7684\u76f4\u89d2\u5750\u6807\u8fd0\u7b97
\u8bbea\uff1d \uff0cb\uff1d \u5219
(1)a\uff0bb\uff1d \uff1b
(2)a\uff0db\uff1d \uff1b
(3)\u03bba\uff1d (\u03bb\u2208R)\uff1b
(4)a•b\uff1d \uff1b
123.\u8bbeA \uff0cB \uff0c\u5219
= .
124\uff0e\u7a7a\u95f4\u7684\u7ebf\u7ebf\u5e73\u884c\u6216\u5782\u76f4
\u8bbe \uff0c \uff0c\u5219
\uff1b
.
125.\u5939\u89d2\u516c\u5f0f
\u8bbea\uff1d \uff0cb\uff1d \uff0c\u5219
cos\u3008a\uff0cb\u3009= .
\u63a8\u8bba \uff0c\u6b64\u5373\u4e09\u7ef4\u67ef\u897f\u4e0d\u7b49\u5f0f.
126. \u56db\u9762\u4f53\u7684\u5bf9\u68f1\u6240\u6210\u7684\u89d2
\u56db\u9762\u4f53 \u4e2d, \u4e0e \u6240\u6210\u7684\u89d2\u4e3a ,\u5219
.
127\uff0e\u5f02\u9762\u76f4\u7ebf\u6240\u6210\u89d2
=
\uff08\u5176\u4e2d \uff08 \uff09\u4e3a\u5f02\u9762\u76f4\u7ebf \u6240\u6210\u89d2\uff0c \u5206\u522b\u8868\u793a\u5f02\u9762\u76f4\u7ebf \u7684\u65b9\u5411\u5411\u91cf\uff09
128.\u76f4\u7ebf \u4e0e\u5e73\u9762\u6240\u6210\u89d2
( \u4e3a\u5e73\u9762 \u7684\u6cd5\u5411\u91cf).
129.\u82e5 \u6240\u5728\u5e73\u9762\u82e5 \u4e0e\u8fc7\u82e5 \u7684\u5e73\u9762 \u6210\u7684\u89d2 ,\u53e6\u4e24\u8fb9 , \u4e0e\u5e73\u9762 \u6210\u7684\u89d2\u5206\u522b\u662f \u3001 , \u4e3a \u7684\u4e24\u4e2a\u5185\u89d2\uff0c\u5219
.
\u7279\u522b\u5730,\u5f53 \u65f6,\u6709
.
130.\u82e5 \u6240\u5728\u5e73\u9762\u82e5 \u4e0e\u8fc7\u82e5 \u7684\u5e73\u9762 \u6210\u7684\u89d2 ,\u53e6\u4e24\u8fb9 , \u4e0e\u5e73\u9762 \u6210\u7684\u89d2\u5206\u522b\u662f \u3001 , \u4e3a \u7684\u4e24\u4e2a\u5185\u89d2\uff0c\u5219
.
\u7279\u522b\u5730,\u5f53 \u65f6,\u6709
.
131.\u4e8c\u9762\u89d2 \u7684\u5e73\u9762\u89d2
\u6216 \uff08 \uff0c \u4e3a\u5e73\u9762 \uff0c \u7684\u6cd5\u5411\u91cf\uff09.
132.\u4e09\u4f59\u5f26\u5b9a\u7406
\u8bbeAC\u662f\u03b1\u5185\u7684\u4efb\u4e00\u6761\u76f4\u7ebf\uff0c\u4e14BC\u22a5AC\uff0c\u5782\u8db3\u4e3aC\uff0c\u53c8\u8bbeAO\u4e0eAB\u6240\u6210\u7684\u89d2\u4e3a \uff0cAB\u4e0eAC\u6240\u6210\u7684\u89d2\u4e3a \uff0cAO\u4e0eAC\u6240\u6210\u7684\u89d2\u4e3a \uff0e\u5219 .
133. \u4e09\u5c04\u7ebf\u5b9a\u7406
\u82e5\u5939\u5728\u5e73\u9762\u89d2\u4e3a \u7684\u4e8c\u9762\u89d2\u95f4\u7684\u7ebf\u6bb5\u4e0e\u4e8c\u9762\u89d2\u7684\u4e24\u4e2a\u534a\u5e73\u9762\u6240\u6210\u7684\u89d2\u662f , ,\u4e0e\u4e8c\u9762\u89d2\u7684\u68f1\u6240\u6210\u7684\u89d2\u662f\u03b8\uff0c\u5219\u6709 ;
(\u5f53\u4e14\u4ec5\u5f53 \u65f6\u7b49\u53f7\u6210\u7acb).
134.\u7a7a\u95f4\u4e24\u70b9\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f
\u82e5A \uff0cB \uff0c\u5219
= .
135.\u70b9 \u5230\u76f4\u7ebf \u8ddd\u79bb
(\u70b9 \u5728\u76f4\u7ebf \u4e0a\uff0c\u76f4\u7ebf \u7684\u65b9\u5411\u5411\u91cfa= \uff0c\u5411\u91cfb= ).
136.\u5f02\u9762\u76f4\u7ebf\u95f4\u7684\u8ddd\u79bb
( \u662f\u4e24\u5f02\u9762\u76f4\u7ebf\uff0c\u5176\u516c\u5782\u5411\u91cf\u4e3a \uff0c \u5206\u522b\u662f \u4e0a\u4efb\u4e00\u70b9\uff0c \u4e3a \u95f4\u7684\u8ddd\u79bb).
137.\u70b9 \u5230\u5e73\u9762 \u7684\u8ddd\u79bb
\uff08 \u4e3a\u5e73\u9762 \u7684\u6cd5\u5411\u91cf\uff0c \u662f\u7ecf\u8fc7\u9762 \u7684\u4e00\u6761\u659c\u7ebf\uff0c \uff09.
138.\u5f02\u9762\u76f4\u7ebf\u4e0a\u4e24\u70b9\u8ddd\u79bb\u516c\u5f0f
.
.
\uff08 \uff09.
(\u4e24\u6761\u5f02\u9762\u76f4\u7ebfa\u3001b\u6240\u6210\u7684\u89d2\u4e3a\u03b8\uff0c\u5176\u516c\u5782\u7ebf\u6bb5 \u7684\u957f\u5ea6\u4e3ah.\u5728\u76f4\u7ebfa\u3001b\u4e0a\u5206\u522b\u53d6\u4e24\u70b9E\u3001F\uff0c , , ).
139.\u4e09\u4e2a\u5411\u91cf\u548c\u7684\u5e73\u65b9\u516c\u5f0f
140. \u957f\u5ea6\u4e3a \u7684\u7ebf\u6bb5\u5728\u4e09\u6761\u4e24\u4e24\u4e92\u76f8\u5782\u76f4\u7684\u76f4\u7ebf\u4e0a\u7684\u5c04\u5f71\u957f\u5206\u522b\u4e3a \uff0c\u5939\u89d2\u5206\u522b\u4e3a ,\u5219\u6709
.
\uff08\u7acb\u4f53\u51e0\u4f55\u4e2d\u957f\u65b9\u4f53\u5bf9\u89d2\u7ebf\u957f\u7684\u516c\u5f0f\u662f\u5176\u7279\u4f8b\uff09.
141. \u9762\u79ef\u5c04\u5f71\u5b9a\u7406
.
(\u5e73\u9762\u591a\u8fb9\u5f62\u53ca\u5176\u5c04\u5f71\u7684\u9762\u79ef\u5206\u522b\u662f \u3001 \uff0c\u5b83\u4eec\u6240\u5728\u5e73\u9762\u6240\u6210\u9510\u4e8c\u9762\u89d2\u7684\u4e3a ).
142. \u659c\u68f1\u67f1\u7684\u76f4\u622a\u9762
\u5df2\u77e5\u659c\u68f1\u67f1\u7684\u4fa7\u68f1\u957f\u662f ,\u4fa7\u9762\u79ef\u548c\u4f53\u79ef\u5206\u522b\u662f \u548c ,\u5b83\u7684\u76f4\u622a\u9762\u7684\u5468\u957f\u548c\u9762\u79ef\u5206\u522b\u662f \u548c ,\u5219
\u2460 .
\u2461 .
143\uff0e\u4f5c\u622a\u9762\u7684\u4f9d\u636e
\u4e09\u4e2a\u5e73\u9762\u4e24\u4e24\u76f8\u4ea4\uff0c\u6709\u4e09\u6761\u4ea4\u7ebf\uff0c\u5219\u8fd9\u4e09\u6761\u4ea4\u7ebf\u4ea4\u4e8e\u4e00\u70b9\u6216\u4e92\u76f8\u5e73\u884c.
144\uff0e\u68f1\u9525\u7684\u5e73\u884c\u622a\u9762\u7684\u6027\u8d28
\u5982\u679c\u68f1\u9525\u88ab\u5e73\u884c\u4e8e\u5e95\u9762\u7684\u5e73\u9762\u6240\u622a\uff0c\u90a3\u4e48\u6240\u5f97\u7684\u622a\u9762\u4e0e\u5e95\u9762\u76f8\u4f3c\uff0c\u622a\u9762\u9762\u79ef\u4e0e\u5e95\u9762\u9762\u79ef\u7684\u6bd4\u7b49\u4e8e\u9876\u70b9\u5230\u622a\u9762\u8ddd\u79bb\u4e0e\u68f1\u9525\u9ad8\u7684\u5e73\u65b9\u6bd4\uff08\u5bf9\u5e94\u89d2\u76f8\u7b49\uff0c\u5bf9\u5e94\u8fb9\u5bf9\u5e94\u6210\u6bd4\u4f8b\u7684\u591a\u8fb9\u5f62\u662f\u76f8\u4f3c\u591a\u8fb9\u5f62\uff0c\u76f8\u4f3c\u591a\u8fb9\u5f62\u9762\u79ef\u7684\u6bd4\u7b49\u4e8e\u5bf9\u5e94\u8fb9\u7684\u6bd4\u7684\u5e73\u65b9\uff09\uff1b\u76f8\u5e94\u5c0f\u68f1\u9525\u4e0e\u5c0f\u68f1\u9525\u7684\u4fa7\u9762\u79ef\u7684\u6bd4\u7b49\u4e8e\u9876\u70b9\u5230\u622a\u9762\u8ddd\u79bb\u4e0e\u68f1\u9525\u9ad8\u7684\u5e73\u65b9\u6bd4\uff0e
145.\u6b27\u62c9\u5b9a\u7406(\u6b27\u62c9\u516c\u5f0f)
(\u7b80\u5355\u591a\u9762\u4f53\u7684\u9876\u70b9\u6570V\u3001\u68f1\u6570E\u548c\u9762\u6570F).
\uff081\uff09 =\u5404\u9762\u591a\u8fb9\u5f62\u8fb9\u6570\u548c\u7684\u4e00\u534a.\u7279\u522b\u5730,\u82e5\u6bcf\u4e2a\u9762\u7684\u8fb9\u6570\u4e3a \u7684\u591a\u8fb9\u5f62\uff0c\u5219\u9762\u6570F\u4e0e\u68f1\u6570E\u7684\u5173\u7cfb\uff1a \uff1b
\uff082\uff09\u82e5\u6bcf\u4e2a\u9876\u70b9\u5f15\u51fa\u7684\u68f1\u6570\u4e3a \uff0c\u5219\u9876\u70b9\u6570V\u4e0e\u68f1\u6570E\u7684\u5173\u7cfb\uff1a .
146.\u7403\u7684\u534a\u5f84\u662fR\uff0c\u5219
\u5176\u4f53\u79ef ,
\u5176\u8868\u9762\u79ef \uff0e
147.\u7403\u7684\u7ec4\u5408\u4f53
(1)\u7403\u4e0e\u957f\u65b9\u4f53\u7684\u7ec4\u5408\u4f53:
\u957f\u65b9\u4f53\u7684\u5916\u63a5\u7403\u7684\u76f4\u5f84\u662f\u957f\u65b9\u4f53\u7684\u4f53\u5bf9\u89d2\u7ebf\u957f.
(2)\u7403\u4e0e\u6b63\u65b9\u4f53\u7684\u7ec4\u5408\u4f53:
\u6b63\u65b9\u4f53\u7684\u5185\u5207\u7403\u7684\u76f4\u5f84\u662f\u6b63\u65b9\u4f53\u7684\u68f1\u957f, \u6b63\u65b9\u4f53\u7684\u68f1\u5207\u7403\u7684\u76f4\u5f84\u662f\u6b63\u65b9\u4f53\u7684\u9762\u5bf9\u89d2\u7ebf\u957f, \u6b63\u65b9\u4f53\u7684\u5916\u63a5\u7403\u7684\u76f4\u5f84\u662f\u6b63\u65b9\u4f53\u7684\u4f53\u5bf9\u89d2\u7ebf\u957f.
(3) \u7403\u4e0e\u6b63\u56db\u9762\u4f53\u7684\u7ec4\u5408\u4f53:
\u68f1\u957f\u4e3a \u7684\u6b63\u56db\u9762\u4f53\u7684\u5185\u5207\u7403\u7684\u534a\u5f84\u4e3a ,\u5916\u63a5\u7403\u7684\u534a\u5f84\u4e3a .
148\uff0e\u67f1\u4f53\u3001\u9525\u4f53\u7684\u4f53\u79ef
\uff08 \u662f\u67f1\u4f53\u7684\u5e95\u9762\u79ef\u3001 \u662f\u67f1\u4f53\u7684\u9ad8\uff09.
\uff08 \u662f\u9525\u4f53\u7684\u5e95\u9762\u79ef\u3001 \u662f\u9525\u4f53\u7684\u9ad8\uff09.
149.\u5206\u7c7b\u8ba1\u6570\u539f\u7406\uff08\u52a0\u6cd5\u539f\u7406\uff09
.
150.\u5206\u6b65\u8ba1\u6570\u539f\u7406\uff08\u4e58\u6cd5\u539f\u7406\uff09
.
151.\u6392\u5217\u6570\u516c\u5f0f
= = .( \uff0c \u2208N*\uff0c\u4e14 )\uff0e
\u6ce8:\u89c4\u5b9a .
152.\u6392\u5217\u6052\u7b49\u5f0f
(1\uff09 ;
\uff082\uff09 ;
\uff083\uff09 ;
\uff084\uff09 ;
\uff085\uff09 .
(6) .
153.\u7ec4\u5408\u6570\u516c\u5f0f
= = = ( \u2208N*\uff0c \uff0c\u4e14 ).
154.\u7ec4\u5408\u6570\u7684\u4e24\u4e2a\u6027\u8d28
(1) = ;
(2) + = .
\u6ce8:\u89c4\u5b9a .
155.\u7ec4\u5408\u6052\u7b49\u5f0f
\uff081\uff09 ;
\uff082\uff09 ;
\uff083\uff09 ;
\uff084\uff09 = ;
\uff085\uff09 .
(6) .
(7) .
(8) .
(9) .
(10) .
156.\u6392\u5217\u6570\u4e0e\u7ec4\u5408\u6570\u7684\u5173\u7cfb
.
157\uff0e\u5355\u6761\u4ef6\u6392\u5217
\u4ee5\u4e0b\u5404\u6761\u7684\u5927\u524d\u63d0\u662f\u4ece \u4e2a\u5143\u7d20\u4e2d\u53d6 \u4e2a\u5143\u7d20\u7684\u6392\u5217.
\uff081\uff09\u201c\u5728\u4f4d\u201d\u4e0e\u201c\u4e0d\u5728\u4f4d\u201d
\u2460\u67d0\uff08\u7279\uff09\u5143\u5fc5\u5728\u67d0\u4f4d\u6709 \u79cd\uff1b\u2461\u67d0\uff08\u7279\uff09\u5143\u4e0d\u5728\u67d0\u4f4d\u6709 \uff08\u8865\u96c6\u601d\u60f3\uff09 \uff08\u7740\u773c\u4f4d\u7f6e\uff09 \uff08\u7740\u773c\u5143\u7d20\uff09\u79cd.
\uff082\uff09\u7d27\u8d34\u4e0e\u63d2\u7a7a\uff08\u5373\u76f8\u90bb\u4e0e\u4e0d\u76f8\u90bb\uff09
\u2460\u5b9a\u4f4d\u7d27\u8d34\uff1a \u4e2a\u5143\u5728\u56fa\u5b9a\u4f4d\u7684\u6392\u5217\u6709 \u79cd.
\u2461\u6d6e\u52a8\u7d27\u8d34\uff1a \u4e2a\u5143\u7d20\u7684\u5168\u6392\u5217\u628ak\u4e2a\u5143\u6392\u5728\u4e00\u8d77\u7684\u6392\u6cd5\u6709 \u79cd.\u6ce8\uff1a\u6b64\u7c7b\u95ee\u9898\u5e38\u7528\u6346\u7ed1\u6cd5\uff1b
\u2462\u63d2\u7a7a\uff1a\u4e24\u7ec4\u5143\u7d20\u5206\u522b\u6709k\u3001h\u4e2a\uff08 \uff09\uff0c\u628a\u5b83\u4eec\u5408\u5728\u4e00\u8d77\u6765\u4f5c\u5168\u6392\u5217\uff0ck\u4e2a\u7684\u4e00\u7ec4\u4e92\u4e0d\u80fd\u6328\u8fd1\u7684\u6240\u6709\u6392\u5217\u6570\u6709 \u79cd.
\uff083\uff09\u4e24\u7ec4\u5143\u7d20\u5404\u76f8\u540c\u7684\u63d2\u7a7a
\u4e2a\u5927\u7403 \u4e2a\u5c0f\u7403\u6392\u6210\u4e00\u5217\uff0c\u5c0f\u7403\u5fc5\u5206\u5f00\uff0c\u95ee\u6709\u591a\u5c11\u79cd\u6392\u6cd5\uff1f
\u5f53 \u65f6\uff0c\u65e0\u89e3\uff1b\u5f53 \u65f6\uff0c\u6709 \u79cd\u6392\u6cd5.
\uff084\uff09\u4e24\u7ec4\u76f8\u540c\u5143\u7d20\u7684\u6392\u5217\uff1a\u4e24\u7ec4\u5143\u7d20\u6709m\u4e2a\u548cn\u4e2a\uff0c\u5404\u7ec4\u5143\u7d20\u5206\u522b\u76f8\u540c\u7684\u6392\u5217\u6570\u4e3a .
158\uff0e\u5206\u914d\u95ee\u9898
\uff081\uff09(\u5e73\u5747\u5206\u7ec4\u6709\u5f52\u5c5e\u95ee\u9898)\u5c06\u76f8\u5f02\u7684 \u3001 \u4e2a\u7269\u4ef6\u7b49\u5206\u7ed9 \u4e2a\u4eba\uff0c\u5404\u5f97 \u4ef6\uff0c\u5176\u5206\u914d\u65b9\u6cd5\u6570\u5171\u6709 .
\uff082\uff09(\u5e73\u5747\u5206\u7ec4\u65e0\u5f52\u5c5e\u95ee\u9898)\u5c06\u76f8\u5f02\u7684 • \u4e2a\u7269\u4f53\u7b49\u5206\u4e3a\u65e0\u8bb0\u53f7\u6216\u65e0\u987a\u5e8f\u7684 \u5806\uff0c\u5176\u5206\u914d\u65b9\u6cd5\u6570\u5171\u6709
.
\uff083\uff09(\u975e\u5e73\u5747\u5206\u7ec4\u6709\u5f52\u5c5e\u95ee\u9898)\u5c06\u76f8\u5f02\u7684 \u4e2a\u7269\u4f53\u5206\u7ed9 \u4e2a\u4eba\uff0c\u7269\u4ef6\u5fc5\u987b\u88ab\u5206\u5b8c\uff0c\u5206\u522b\u5f97\u5230 \uff0c \uff0c\u2026\uff0c \u4ef6\uff0c\u4e14 \uff0c \uff0c\u2026\uff0c \u8fd9 \u4e2a\u6570\u5f7c\u6b64\u4e0d\u76f8\u7b49\uff0c\u5219\u5176\u5206\u914d\u65b9\u6cd5\u6570\u5171\u6709 .
\uff084\uff09(\u975e\u5b8c\u5168\u5e73\u5747\u5206\u7ec4\u6709\u5f52\u5c5e\u95ee\u9898)\u5c06\u76f8\u5f02\u7684 \u4e2a\u7269\u4f53\u5206\u7ed9 \u4e2a\u4eba\uff0c\u7269\u4ef6\u5fc5\u987b\u88ab\u5206\u5b8c\uff0c\u5206\u522b\u5f97\u5230 \uff0c \uff0c\u2026\uff0c \u4ef6\uff0c\u4e14 \uff0c \uff0c\u2026\uff0c \u8fd9 \u4e2a\u6570\u4e2d\u5206\u522b\u6709a\u3001b\u3001c\u3001\u2026\u4e2a\u76f8\u7b49\uff0c\u5219\u5176\u5206\u914d\u65b9\u6cd5\u6570\u6709 .
\uff085\uff09(\u975e\u5e73\u5747\u5206\u7ec4\u65e0\u5f52\u5c5e\u95ee\u9898)\u5c06\u76f8\u5f02\u7684 \u4e2a\u7269\u4f53\u5206\u4e3a\u4efb\u610f\u7684 \uff0c \uff0c\u2026\uff0c \u4ef6\u65e0\u8bb0\u53f7\u7684 \u5806\uff0c\u4e14 \uff0c \uff0c\u2026\uff0c \u8fd9 \u4e2a\u6570\u5f7c\u6b64\u4e0d\u76f8\u7b49\uff0c\u5219\u5176\u5206\u914d\u65b9\u6cd5\u6570\u6709 .
\uff086\uff09(\u975e\u5b8c\u5168\u5e73\u5747\u5206\u7ec4\u65e0\u5f52\u5c5e\u95ee\u9898)\u5c06\u76f8\u5f02\u7684 \u4e2a\u7269\u4f53\u5206\u4e3a\u4efb\u610f\u7684 \uff0c \uff0c\u2026\uff0c \u4ef6\u65e0\u8bb0\u53f7\u7684 \u5806\uff0c\u4e14 \uff0c \uff0c\u2026\uff0c \u8fd9 \u4e2a\u6570\u4e2d\u5206\u522b\u6709a\u3001b\u3001c\u3001\u2026\u4e2a\u76f8\u7b49\uff0c\u5219\u5176\u5206\u914d\u65b9\u6cd5\u6570\u6709 .
\uff087\uff09(\u9650\u5b9a\u5206\u7ec4\u6709\u5f52\u5c5e\u95ee\u9898)\u5c06\u76f8\u5f02\u7684 \uff08 \uff09\u4e2a\u7269\u4f53\u5206\u7ed9\u7532\u3001\u4e59\u3001\u4e19\uff0c\u2026\u2026\u7b49 \u4e2a\u4eba\uff0c\u7269\u4f53\u5fc5\u987b\u88ab\u5206\u5b8c\uff0c\u5982\u679c\u6307\u5b9a\u7532\u5f97 \u4ef6\uff0c\u4e59\u5f97 \u4ef6\uff0c\u4e19\u5f97 \u4ef6\uff0c\u2026\u65f6\uff0c\u5219\u65e0\u8bba \uff0c \uff0c\u2026\uff0c \u7b49 \u4e2a\u6570\u662f\u5426\u5168\u76f8\u5f02\u6216\u4e0d\u5168\u76f8\u5f02\u5176\u5206\u914d\u65b9\u6cd5\u6570\u6052\u6709
.
159\uff0e\u201c\u9519\u4f4d\u95ee\u9898\u201d\u53ca\u5176\u63a8\u5e7f
\u8d1d\u52aa\u5229\u88c5\u9519\u7b3a\u95ee\u9898:\u4fe1 \u5c01\u4fe1\u4e0e \u4e2a\u4fe1\u5c01\u5168\u90e8\u9519\u4f4d\u7684\u7ec4\u5408\u6570\u4e3a
.
\u63a8\u5e7f: \u4e2a\u5143\u7d20\u4e0e \u4e2a\u4f4d\u7f6e,\u5176\u4e2d\u81f3\u5c11\u6709 \u4e2a\u5143\u7d20\u9519\u4f4d\u7684\u4e0d\u540c\u7ec4\u5408\u603b\u6570\u4e3a
.
160\uff0e\u4e0d\u5b9a\u65b9\u7a0b \u7684\u89e3\u7684\u4e2a\u6570
(1)\u65b9\u7a0b \uff08 \uff09\u7684\u6b63\u6574\u6570\u89e3\u6709 \u4e2a.
(2) \u65b9\u7a0b \uff08 \uff09\u7684\u975e\u8d1f\u6574\u6570\u89e3\u6709 \u4e2a.
(3) \u65b9\u7a0b \uff08 \uff09\u6ee1\u8db3\u6761\u4ef6 ( , )\u7684\u975e\u8d1f\u6574\u6570\u89e3\u6709 \u4e2a.
(4) \u65b9\u7a0b \uff08 \uff09\u6ee1\u8db3\u6761\u4ef6 ( , )\u7684\u6b63\u6574\u6570\u89e3\u6709 \u4e2a.
161.\u4e8c\u9879\u5f0f\u5b9a\u7406 ;
\u4e8c\u9879\u5c55\u5f00\u5f0f\u7684\u901a\u9879\u516c\u5f0f
.
162.\u7b49\u53ef\u80fd\u6027\u4e8b\u4ef6\u7684\u6982\u7387
.
163.\u4e92\u65a5\u4e8b\u4ef6A\uff0cB\u5206\u522b\u53d1\u751f\u7684\u6982\u7387\u7684\u548c
P(A\uff0bB)=P(A)\uff0bP(B)\uff0e
164. \u4e2a\u4e92\u65a5\u4e8b\u4ef6\u5206\u522b\u53d1\u751f\u7684\u6982\u7387\u7684\u548c
P(A1\uff0bA2\uff0b\u2026\uff0bAn)=P(A1)\uff0bP(A2)\uff0b\u2026\uff0bP(An)\uff0e
165.\u72ec\u7acb\u4e8b\u4ef6A\uff0cB\u540c\u65f6\u53d1\u751f\u7684\u6982\u7387
P(A•B)= P(A)•P(B).
166.n\u4e2a\u72ec\u7acb\u4e8b\u4ef6\u540c\u65f6\u53d1\u751f\u7684\u6982\u7387
P(A1• A2•\u2026• An)=P(A1)• P(A2)•\u2026• P(An)\uff0e
167.n\u6b21\u72ec\u7acb\u91cd\u590d\u8bd5\u9a8c\u4e2d\u67d0\u4e8b\u4ef6\u6070\u597d\u53d1\u751fk\u6b21\u7684\u6982\u7387
余弦定理 b^2=a^2+c^2-2accosB 注：角B是边a和边c的夹角
圆的标准方程 (x-a)^2+(y-b)^2=^r2 注：（a,b）是圆心坐标
圆的一般方程 x^2+y^2+Dx+Ey+F=0 注：D^2+E^2-4F>0
抛物线标准方程 y^2=2px y^2=-2px x^2=2py x^2=-2py
直棱柱侧面积 S=c*h 斜棱柱侧面积 S=c'*h
正棱锥侧面积 S=1/2c*h' 正棱台侧面积 S=1/2(c+c')h'
圆台侧面积 S=1/2(c+c')l=pi(R+r)l 球的表面积 S=4pi*r2
圆柱侧面积 S=c*h=2pi*h 圆锥侧面积 S=1/2*c*l=pi*r*l
弧长公式 l=a*r a是圆心角的弧度数r >0 扇形面积公式 s=1/2*l*r
锥体体积公式 V=1/3*S*H 圆锥体体积公式 V=1/3*pi*r2h
斜棱柱体积 V=S'L 注：其中,S'是直截面面积， L是侧棱长
柱体体积公式 V=s*h 圆柱体 V=pi*r2h
倍角公式
tan2A=2tanA/[1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2
半角公式
sin(A/2)=√((1-cosA)/2) sin(A/2)=-√((1-cosA)/2)
cos(A/2)=√((1+cosA)/2) cos(A/2)=-√((1+cosA)/2)
tan(A/2)=√((1-cosA)/((1+cosA)) tan(A/2)=-√((1-cosA)/((1+cosA))
cot(A/2)=√((1+cosA)/((1-cosA)) cot(A/2)=-√((1+cosA)/((1-cosA))
和差化积
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B) )
2cosAcosB=cos(A+B)-sin(A-B)
-2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB=2sin((A+B)/2)cos((A-B)/2
cosA+cosB=2cos((A+B)/2)sin((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB
某些数列前n项和
1+2+3+4+5+6+7+8+9+…+n=n(n+1)/2
1+3+5+7+9+11+13+15+…+(2n-1)=n2
2+4+6+8+10+12+14+…+(2n)=n(n+1) 5
1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+…+n^2=n(n+1)(2n+1)/6
1^3+2^3+3^3+4^3+5^3+6^3+…n^3=n2(n+1)2/4
1*2+2*3+3*4+4*5+5*6+6*7+…+n(n+1)=n(n+1)(n+2)/3
常用导数公式
1.y=c(c为常数) y'=0
2.y=x^n y'=nx^(n-1)
3.y=a^x y'=a^xlna
y=e^x y'=e^x
4.y=logax y'=logae/x
y=lnx y'=1/x
5.y=sinx y'=cosx
6.y=cosx y'=-sinx
7.y=tanx y'=1/cos^2x
8.y=cotx y'=-1/sin^2x
9.y=arcsinx y'=1/√1-x^2
10.y=arccosx y'=-1/√1-x^2
11.y=arctanx y'=1/1+x^2
12.y=arccotx y'=-1/1+x^2
2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+…+n^2=n(n+1)(2n+1)/6
1^3+2^3+3^3+4^3+5^3+6^3+…n^3=n2(n+1)2/4
1*2+2*3+3*4+4*5+5*6+6*7+…+n(n+1)=n(n+1)(n+2)/3
常用导数公式
1.y=c(c为常数) y'=0
2.y=x^n y'=nx^(n-1)
3.y=a^x y'=a^xlna
y=e^x y'=e^x
4.y=logax y'=logae/x
y=lnx y'=1/x
5.y=sinx y'=cosx
6.y=cosx y'=-sinx
7.y=tanx y'=1/cos^2x
8.y=cotx y'=-1/sin^2x
9.y=arcsinx y'=1/√1-x^2
10.y=arccosx y'=-1/√1-x^2
11.y=arctanx y'=1/1+x^2
12.y=arccotx y'=-1/1+x^2
自己从网上搜搜就行了么。数学公式死记硬背是不行的，很多都需要在理解的基础上记忆。做题时最忌看着公式做题，这样永远都掌握不好
小学数学公式大全（完整版2），数学学得好不好全靠它了！
高中会考是为了拿高中毕业证的，与高考没有任何关系的
绛旓細楂樹腑涓浜涙瘮杈冩湁鐢ㄧ殑鏁板鍏紡銆傛渶濂芥湁鍒嗙被銆傞傚悎鏂囩鏁板銆1.璇卞鍏紡 sin(-a)=-sin(a) cos(-a)=cos(a) sin(蟺2-a)=cos(a) cos(蟺2-a)=sin(a) sin(蟺2+a)=cos(a) cos(蟺2+a)=-sin(a) sin(蟺-a)=sin(a) cos(蟺-a)=-cos
绛旓細楂樹腑鏁板鍏紡鎶涚墿绾:y = ax *+ bx + c 灏辨槸y绛変簬ax 鐨勫钩鏂瑰姞涓 bx鍐嶅姞涓 c a > 0鏃跺紑鍙ｅ悜涓 a < 0鏃跺紑鍙ｅ悜涓 c = 0鏃舵姏鐗╃嚎缁忚繃鍘熺偣 b = 0鏃舵姏鐗╃嚎瀵圭О杞翠负y杞 杩樻湁椤剁偣寮弝 = a(x+h)* + k 灏辨槸y绛変簬a涔樹互(x+h)鐨勫钩鏂+k -h鏄《鐐瑰潗鏍囩殑x k鏄《鐐瑰潗鏍囩殑y 涓鑸敤浜庢眰...
绛旓細楂樹腑鏁板鍏紡濡備笅锛1銆乧os(A-B) = cosAcosB+sinAsinB銆2銆乧ot(A-B) = (cotAcotB+1)/(cotB-cotA)銆3銆乼an3a = tan a • tan(蟺/3+a)• tan(蟺/3-a)銆4銆乻in(A/2)=鈭((1-cosA)/2) sin(A/2)=-鈭((1-cosA)/2)銆5銆乧os(a)+cos(b) = 2cos[(a+b)/2]...
绛旓細14涓鏁鍏紡濡備笅銆1銆亂=cy=02銆亂=伪^渭y=渭伪^锛埼-1锛3銆亂=a^xy=a^xlnay=e^xy=e^4銆亂=logaxy=loga锛宔/xy=lnxy=1/x5銆亂=sinxy=cosx6銆亂=cosxy=-sinx7銆亂=tanxy=锛坰ecx锛塣2=1/锛坈osx锛塣2銆8銆亂=cotxy=-锛坈scx锛塣2=-1/锛坰inx锛塣29銆亂=arcsinxy=1/鈭氾紙1-x^2...
绛旓細鍦ㄦ暟瀛﹂噷鍏紡鐨勯噸瑕佹т笉瑷鑰屽柣锛岄偅涔堥珮涓暟瀛﹀叕寮忛兘鏈夊摢浜涘憿?涓嬮潰鏄敱鎴戜负澶у鏁寸悊鐨勨楂樹腑鏁板鍏紡澶у叏(瀹屾暣鐗)绮鹃夆濓紝浠呬緵鍙傝冿紝娆㈣繋澶у闃呰鏈枃銆傞珮涓暟瀛﹀叕寮忓ぇ鍏(瀹屾暣鐗)绮鹃 1銆佷袱瑙掑拰鍏紡 sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA cos(A+B)=cosAcosB-sinAsinB cos(A-B...
绛旓細楂樹腑鏁板甯哥敤鐨鍏紡濡備笅锛1銆佸潎鍊间笉绛夊紡锛歛+b鈮2鈭歛b锛坅鈮0锛宐鈮0锛夛紝杩欎釜鍏紡涔熻绉颁负绠楁湳骞冲潎鏁颁笌鍑犱綍骞冲潎鏁扮殑涓嶇瓑寮忋傚畠琛ㄦ槑瀵逛簬浠绘剰瀹炴暟a鍜宐锛屽畠浠殑鍜宎+b鑷冲皯绛変簬瀹冧滑鐨勫嚑浣曞钩鍧囨暟2鈭歛b銆傚綋涓斾粎褰揳=b鏃讹紝绛夊彿鎴愮珛銆傝繖涓叕寮忓湪姹傝В鏈鍊奸棶棰樻椂闈炲父鏈夌敤锛屽彲浠ョ敤鏉ョ‘瀹氭煇浜涘嚱鏁扮殑鏈灏忓笺2銆...
绛旓細楂樹腑鏁板鍩烘湰鍏紡 鎶涚墿绾匡細y = ax + bx + c a > 0鏃跺紑鍙ｅ悜涓奱 < 0鏃跺紑鍙ｅ悜涓 c = 0鏃舵姏鐗╃嚎缁忚繃鍘熺偣 b = 0鏃舵姏鐗╃嚎瀵圭О杞翠负y杞 杩樻湁椤剁偣寮弝 = a锛坸+h锛+ k -h鏄《鐐瑰潗鏍囩殑x k鏄《鐐瑰潗鏍囩殑y涓鑸敤浜庢眰鏈澶у间笌鏈灏忓 鎶涚墿绾挎爣鍑嗘柟绋:y^2=2px 瀹冭〃绀烘姏鐗╃嚎鐨勭劍鐐瑰湪x鐨勬鍗婅酱涓...
绛旓細瀛﹀ソ鏁板鐨勭涓姝ユ槸鈥滆浣忓苟娣卞埢鐞嗚В鍏紡鈥,杩欐牱鍦ㄥ仛棰樻椂鎵嶄細鏈夎揣锛屼互涓嬫槸楂樹腑鏁板鎵鏈夊叕寮忥細閮芥槸浜涙渶鍩虹鐨勪笢瑗匡紝瀛︿範濂界殑鍚屽鍙互鐪嬬湅鑷繁鏈夊摢浜涚偣鑷繁娌℃帉鎻″ソ锛屽熀纭涓嶅ソ鐨勫悓瀛﹀彲浠ュ皾璇曟妸瀹冩妱涓嬫潵锛屽湪瀛︿範杩囩▼涓紝娌′簨鐨勬椂鍊欐嬁鍑烘潵缈荤炕鐪嬶紝缁濆瀵逛綘澶ф湁甯姪銆1銆侀傜敤鏉′欢[鐩寸嚎杩囩劍鐐筣锛屽繀鏈塭cosA=...
绛旓細2 楂樹腑鏁板鍏紡 23 瑙掕竟瑙掑叕鐞( ASA)鏈変袱瑙掑拰瀹冧滑鐨勫す杈瑰搴旂浉绛夌殑涓や釜涓夎褰㈠叏绛 24 鎺ㄨ(AAS) 鏈変袱瑙掑拰鍏朵腑涓瑙掔殑瀵硅竟瀵瑰簲鐩哥瓑鐨勪袱涓笁瑙掑舰鍏ㄧ瓑 25 杈硅竟杈瑰叕鐞(SSS) 鏈変笁杈瑰搴旂浉绛夌殑涓や釜涓夎褰㈠叏绛 26 鏂滆竟銆佺洿瑙掕竟鍏悊(HL) 鏈夋枩杈瑰拰涓鏉＄洿瑙掕竟瀵瑰簲鐩哥瓑鐨勪袱涓洿瑙掍笁瑙掑舰鍏ㄧ瓑 27 瀹氱悊1 鍦ㄨ鐨勫钩鍒嗙嚎...
绛旓細椤剁偣鍧愭爣绛変俊鎭紝浠庤屾洿濂藉湴鐞嗚В浜屾鏇茬嚎鐨勬ц川鍜岀壒寰併3銆侀煢杈惧畾鐞嗚繕鍙互鐢ㄤ簬瑙ｅ喅涓浜涘叾浠鏁板闂銆備緥濡傦紝鍦ㄦ暟鍒椾腑锛屾垜浠彲浠ュ埄鐢ㄩ煢杈惧畾鐞嗘潵姹傝В鏁板垪鐨勯氶」鍏紡锛涘湪瑙ｆ瀽鍑犱綍涓紝鎴戜滑鍙互浣跨敤闊﹁揪瀹氱悊鏉ユ眰瑙ｇ洿绾夸笌鏇茬嚎鐨勪氦鐐瑰潗鏍囥傝繕鍙互鍒╃敤闊﹁揪瀹氱悊鍙互鏂逛究鍦版眰瑙ｅ嚭瀵圭О鏂圭▼缁勭殑瑙ｃ
