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?????????5?????(??)
??5?????
1??????????C??a?b?c????????C????R????C??????????
abc
???2R? sin?sin?sinC
2????????????a?2Rsin??b?2Rsin??c?2RsinC?
abc?sin???sinC???a:b:c?sin?:sin?:sinC? 2R2R2Ra?b?cabc
?????
sin??sin??sinCsin?sin?sinC
?sin??
????????????????1?????????????????????2????????????????
????????????????????????????????????????? ??????ABC????a?b?A?A?????B?????????????? ????????a??C??????????AD?????
?????B??? ???????B???? ???????B????? ??????CD=bsinA,?a???? ?a<bsinA??B??
?bsinA<a?b,?B??? ?a=bsinA?a>b??B???
???A??????????????? 3?????????S???C?
111
bcsin??absinC?acsin?? 222
2
2
2
2
2
2
4??????????C???a?b?c?2bccos??b?a?c?2accos??
c2?a2?b2?2abcosC?
b2?c2?a2a2?c2?b2a2?b2?c2
5?????????cos???cos???cosC??
2bc2ab2ac
(????????????1???????????????2???????)
C????b?6?????????????a?????a?b?c??C?90? c????C??????
??a?b?c??C?90???a?b?c??C?90? ??????????????????????A?B,
1
2
2
2
222?
?222?
C?D??? ????ACB=75, ?BCD=45, ?ADC=30,
?ADB=45(A?B?C?D??????)?????A?B?????? ???????
?????????? ????????????.
??????????????????. ??????????????????. ????????????????. 7?????????????????? 8??????????????? 9?????????????? 10??????????????
11????????2?????????????????????an+1>an?? 12????????2?????????????????????an+1<an?? 13???????????????an+1=an??
14????????2???????????????????????????? 15??????????????an???n????n?????????
16??????????????an??????an?1??????????????
17?????????2????????????????????????????????????????????????????:an?1?an?d????????????????????? ? an?an?1?d(n?2,d???)?2an?an?1?an?1(n?2) ?an?kn?b(n,k???
18?????a???b????????????????????????a?b???????
O
O
O
O
b?
a?c
???b?a?c?????? 2
19??????
?an?????a????d??a
1
n
?a1??n?1?d?
?
an?a1
20??????????an?am??n?m?d??a1?an??n?1?d??d?
n?1
2
an?aman?a1
?1??d??n?
n?md
?
21???an????????m?n?p?q?m?n?p?q??*???am?an?????2n?p?q?n?p?q??*???2an
?ap?aq???an???
?ap?aq?
n?a1?an?
Sn?
2
??
22???????n???????
Sn?na1?
n?n?1?
d??2
sn?a1?a2???an
*
23???????n???????????2nn????S2n
??
?n?an?an?1???S??S??nd?
S?a
?nS?an?1
?
*
?????2n?1n????S2n?1??2n?1?an??S??S??an?
??
S?n
???S??nan??
S?n?1
? S???n?1?an?
24?????????2?????????????????????????????????????????????????????
an?1
?q???????????????0????????an
?????
????????????????????
2
?an?an?1q(n?2,q???,??0)?an?an?1?an?1(n?2?anan?1an?1?0)
?an?cqn(c,q?????).
????{an}???????????{logxan}?x?1??????.
25??a?b???????G??a?G?b???????G??a?b???????G?ab???G?a?b??????????G?ab????a?G?b?????a?G?b?G?ab? 26???????an?????a1????q??an?a1qn?1?
??n?1?n?m
a?aqa?aq27??????????n??1??qn?1mn
2
22
ann?man
q???? ?
ama1
*
28???an????????m?n?p?q?m?n?p?q?????am?an?ap?aq???an????
3
????2n?p?q?n?p?q??*???an
2
?ap?aq?
?na1?q?1?
?
29??????an???n???????Sn??a1?1?qn?a?aq??sn
?1n?q?1??
1?q?1?q
?s1?a1(n?1)
30???????{an}??n??Sn???an????an??
s?s(n?2)n?1?n
?a1?a2???an
[?]? ?an?a1??n?1?d?nd??a1?d??d????????????????????????????????d??0????????????. ???{an}?n??Sn?An2?Bn???n2??a1?
?
?d?
?2?
?
d?d
?n ?????????????????????2?2
d????????????????d???????????????.
?????????????????????.???????????????? ?????????????????
???????n???Sn??d?0??????. ?????Sn??????n???????? ????an?0,an?1?0????n?????Sn??????????????????????
??????????????????????????????n???????n?????????????????????????? ???1??????????
d2d
n?(a1?)n??????????n??. 22
???? .
???????????n??????
4
??????????????n,m?,(m,n),(m+n,)?????
???????????????????=0??????????????
???????????????????????????? ???2?????
??
??n???
??
?n????
???
????????n????????n?????=?
????=????????????
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?????????????????????????????????????????
?
????????????B??A??????
??
???????????????????????????????????n??????????111
n???????????????. ???1?,3,...(2n?1)n,...
242
??????????????????????????????????????????????
5
?????????? ?????????
???? ??????
????????????
???????????
abc
???2R 1??????????C??a?b?c????????C???????
sin?sin?sinC
(R????C???????)
2???????????
?a?2Rsin??b?2Rsin??c?2RsinC? ?sin??
cab
?sin???sinC??
2R2R2R
?a:b:c?sin?:sin?:sinC? 3?????????S???C?
111
bcsin??absinC?acsin?? 222
2
2
2
b2?c2?a2
4??????????C???a?b?c?2bccos?????cosA?
2bc
a2?c2?b2
222cosB?b?a?c?2accosB????2ac
a2?b2?c2
c?a?b?2abcosC????cosC?
2ab
2
2
2
??????
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
1??????????
?1?????????180?
?2?????????????????????????????
?3?????????????????
?4??????,a=2RsinA,b=2RsinB,c=2RsinC???R??ABC?????. ?5???????:2bccosA=b2?c2?a2. ?6??????????:S=
1111
ah,S=absinC=bcsinA=acsinB , S=P(P?a)?(P?b)(P?c)?2222
??h?BC????P????.
2????????????????????????
?1??????????????????????.
?2?????????????????????????????. ?3??????????????????.
?4??????????????????????????????. ?5????????????????????????????????.
3?????????????????
?????????????????.
4??????????
?1?????
????ABC??A+B+C=????sin(A+B)=sinC?cos(A+B)=?cosC?tan(A+B)=?tanC?
sin
A?BCA?BC
?cos,cos?sin? 2222
?2???????????????????????????
r??????????p?????
?3???ABC??????????A??B??C??????????????B=60??ABC??????????????A??B??C??????a?b?c?????.
?????????
1.??????
???????????????????????h?????l????????i????????????????????i?tan?.
2.??????
h
????????????????????????????????????????????????????????????????.
3. ???
?????????????????????B???????.
????????????????????????????????????????????????????????
4. ????
????????????.
5.???
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??
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1???????
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??????????????N????????????????????????????????????????.
?
2???????
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?1? ????????????????????? ?2? ????????????????????.
3??????
?????an???n?an???n?????????????????an?f?n??????????????????????????????????????.
4?????????
?????????an??
??????????????????????an?1?an?????????????; ??????????????????????an?1?an?????????????; ?????an???????????????????.
5??????
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1?????????
???????????????????????????????????????????????????????.
?an?1?an?d???????????????????????????.
2???????????
??????an?????a1????d????????
an?a1??n?1?d?am??n?m?d,?n?m?N??.
3??????
?1??a?A?b???????A??a?b???????A=
a?b
; 2
?2?????an????????an,an?1,an?2???????an?1?an?an?2???????
an?1=
an?an?2a?an?2
???????an???an?1=n?????an??????. 22
?????????1-5_?????+????
????1-5???????
??1? ????1????????1?????????????????????
?2?????????????? ?3???????????????????
2??????????????x?A??? x?B???A?B??????A?B
?????A?B??????B????????????A??A?B???????A?B ???????A?B,B?A,?
?
A?B
3. ???????????? ????? ????
4???????????????A?????B?????????????? A?B
??????A???B?????????????????A?B
??????U??????????A????????????
??CUA
5???{a1,a2,?,an}???????2 ??????21???????2 1?? 6.??????????N ?????N ????Z?????Q ????R ????????
1???? ??? <=> f ( x ) = f ( x ) ???? <=> f (x ) = f ( x )??????? 2?????1??????????????????? ?2?????????y????????
?3???????????????????????????? ?4????????????y??????????????? ????????
1??????????D???f ( x )?????x1, x2?D??x1 < x2
? f ( x1 ) < f ( x 2 ) <=>f ( x1 ) f ( x2 ) < 0 <=> f ( x )???? ? f ( x1 ) > f ( x 2 ) <=>f ( x1 ) f ( x2 ) > 0 <=> f ( x )???? 2?????????: ????
??????y = ax2 +bx + c?a?0????
*n
n
n
?b4ac?b2?b4ac?b2
1???????????2a,4a??? ????x??2a????????4a
??
2.?????????????
(1)???f(x)?ax2?bx?c(a?0); (2)???f(x)?a(x?h)2?k(a?0); (3)???f(x)?a(x?x1)(x?x2)(a?0). ????????? 1????????
?1?a m ? a n = a m + n ??2?a?a?a
n
m
n
m?n
??3?( a m ) n = a m n ?4?( ab ) n = a n ? b n
n
?11an?a??nn0mma??5? ???n?6?a = 1 ( a?0)?7? ?8??9? a?aa?nnabb??a
n
2??????
?1
?n?a.
?2??n
?a? ?n
?|a|??
4?????y = a x (a > 0?a?1)????
?1?????R ? ???( 0 , +?)?2???????0?1?
5.??????????? logaN?b?ab?N(a?0,a?1,N?0). ????????? 1????????
?1?a b = N <=> b = log a N?2?log a 1 = 0?3?log a a = 1?4?log a a b = b?5?a
log a N
?a,a?0
.
??a,a?0
= N
?6?log a (MN) = log a M + log a N ?7?log a (
M
) = log a M -- log a N N
?8?log a N b = b log a N ?9??????log a N =
n
logbN
logba
?10??? logamb??11?log a N =
n
logab(a?0,?a?1,m,n?0,?m?1,n?1, N?0). m
1
?12??????lg N = log 10 N ?13??????ln A = log e A
logNa
??? e = 2.71828?? 2?????y = log a x (a > 0?a?1)???? ?1?????( 0 , +?) ? ???R?2???????1?0?
?????y = x a ???:?1? ?? a ??????????????? .
??? y = x y?
2
x?x y?
12
1
?x?1 x
?.?????????y?f(x)?????a???b???? ????y?f(x?a)?b???? ???????????? ?. ????????
???????????N???????p??????x????y??y?N1(?p)????????1.?????y?f(x)???f(x)?0?X?y?f(x)?????
x
.
y?f(x)????X???????????
2.??????????????y?f(x)????a,b????????????? ?????f(a)?f(b)?0???y?f(x)????a,b?????????c??a,b?? ??f(c)?0???C?????
3.????????????????????
?1??????a,b????f(a)?f(b)?0;(2)??a,b????x1?
a?b
2
?3???f(x1)??f(x1)?0??x1???????f(a)?f(x1)?0????
x0??a,x1? ??f(x1)?f(b)?0????x0??x1,b??
?4?????????????a?b???????a?b??a,b??????? ????2???4?
??2??????? 1?????????k = tan?=
y2?y1
?? ? 90?x 1?x 2?
x2?x1
2???????1???? y = k x + b,k?? ??2???? y y 0 = k ( x x 0 ) ?k??? ?3????
y?y1x?x1xy
?x1?x2,y1?y2? ?4???? ??1?a?0,b?0? ?
aby2?y1x2?x1
?5????Ax?By?c?0(A,B????0? 3???????????
4??????????P1 ( x 1 , y 1 ) ?P 2 ( x 2 , y 2 )?? | P1 P2 | =5??P ( x 0 , y 0 )???l ?A x + B y + C = 0????d?
x1?x22?y1?y22
2
2
Ax0?By0?CA?B
7?????
8.????????
?P(x0,y0)??(x?a)2?(y?b)2?r2?????????d?
? d?r??P???;d?r??P???;d?r??P???. 9.?????????(?????????d)
222
??Ax?By?C?0??(x?a)?(y?b)?r????????:
d?r??????0;d?r??????0;d?r??????0.
10.???????????
????????O1?O2??????r1?r2?O1O2?d
d?r1?r2????4????; d?r1?r2????3????;
r1?r2?d?r1?r2????2????; d?r1?r2????1????; 0?d?r1?r2????????.
11.??????
(1)???x?y?Dx?Ey?F?0?
??????(x0,y0)????????????????
2
2
D(x0?x)E(y0?y)
??F?0. 22
D(x0?x)E(y0?y)
??F?0????????(x0,y0)???, x0x?y0y?
22
x0x?y0y????????
???????5???????????
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发表于 2019-9-13 23:46:11