反三角函数

反三角函数 --- . ．．．．．．．．．．．．．．． . 1. : PPPPPPPPPP(1) lP,l.P121212 x,xy,yz,z|PP|1111PP,,,P.=;;==. PP,PP,||,1212x,xy,yz,z|PP|2222 (2) : PPPPPPPPPPPPP12122112 PP 1,, >0 <-1 -1<<0 =0 PP2 x，,xy，,y1212,,,(,,,1)(3) :xy. 1，,1，, x，xy，y1212(4) :x,,y,. 22 2. :x .[0?,180?),x,0?. 3. :90?,,k=tan. 4. :P(x,y),P(x,y)111222 y,y21k=(xx);x=x. 1212x,x21 1 15. :(1,k)(cosα,sinα);:(1,-)(sinα,-cosα). k 6. : (1) :P(x,y),ky-y=k(x-x);(lx) 11111 (2) :yb(y(0,b)),ky=kx+b;(lx ) y,yx,x11(3) :P(x,y),P(x,y)(xx,yy)(x=x,111222121212y,yx,x2121y=y),(y-y)(x-x)=(y-y)(x-x). 12121211 xy(4) :xyab(a0,b0).(l，,1abl,) (5) :Ax+By+C=0(A?+B?0,). (6) α x,x，tcos,,0,yytsin,,，0, x,x，at,t，t012,y,y，bt20, (7) αα(sinα,-cosα),p, ,p.:3cosα+4sinα=5tanα. 7. : |Ax，By，C|00(1) :P(x,y)Ax+By+C=0d=. 0022A，B |C,C|12(2) :Ax+By+C=0Ax+By+C=0d=. 1222A，B ，，,0AxByC,1118. :Ax+By+C=0111,Ax，By，C,0222, Ax+By+C=0(AB-AB0). 2221221 9. : (1) l:Ax+By+C=0,l:Ax+By+C=0.ll1111222212 ABC111,,ABC222 (2) l:y=kx+b,l:y=kx+b,ll 11122212 A(x,x)，B(y,y),0Ax，By，C,000(3) P(x,y). 00y,kx，by,y,k(x,x)0010. : (1) l:Ax+By+C=0,l:Ax+By+C=0.ll1111222212 2 (2) l:y=kx+b,l:y=kx+b,ll 11122212 B(x,x),A(y,y),000Ax，By，C,01(3) P(x,y). 00y,kx，by,y,,(x,x)00k 11. : (1) :ll,ll1212 ,ll.(0?,180?) 12 (2) :.(0?,90?] k,kAB,AB终起起终终起(3) :.(,,tan,,1，kkAA，BB121212 k,kAB,AB211221tan,||||(4) :.(,,,1，kkAA，BB121212 12. : (1) ll:(Ax+By+C)+(Ax+By+C)=0(121111222212Ax+By+C+(Ax+By+C)=0(l 1112222 P(x,y):y-y=k(x-x),(x-x)+By-y)=0.0000000 y=kx+b(b00 (4) Ax+By+C=0Ax+By+=0( (5) Ax+By+C=0Bx-Ay+=0( 13. : (1) M(a,b) P(x,y)M(a,b)Q(2a-x,2b-y). F(x,y)M(a,b)F(2a-x,2b-y).() (2) Ax+By+C=0 () :(y=x+b)P(a,b)y=x+bQ. 1. yykxx,,,()Pxy(,)1) lk11111 ykxb,，l yyxx,,11,yy,Pxy(,)Pxy(,)xx,1211122212yyxx,,2121 xy，,1ab、,0ab、ab (AB0).AxByC，，,0 2.. lykxb:,，lykxb:,，(1) 111222 . llkkbb||,,,,llkk,,,,1;1212121212 ABC111lAxByC:0，，,lAxByC:0，，,(2),,AABB,ll||,,,12121111222212ABC222 3 llAABB,,，,0121212 3. kk,21lykxb:,，lykxb:,，tan||,(1),.(,) kk,,1111222121kk，21 ABAB,1221lAxByC:0，，,lAxByC:0，，,tan||,(2),.(,,). AABB，,0111122221212AABB，1212 ,ll,ll. 12122 ,kk21,lltan,lykxb:,，lykxb:,，4.(1).(,)kk,,11211122212，1kk21 ,ABAB1221,tan,lAxByC:0，，,lAxByC:0，，,(2).(,,). AABB，,0111122221212，AABB1212 ,ll,ll. 12122 5 Pxy(,)yykxx,,,()xx,(1)(),000000 Pxy(,)AxxByy()()0,，,,;,AB,k00000 lAxByC:0，，,lAxByC:0，，,11112222()()0AxByCAxByC，，，，，,,lλ1112222 ykxb,， AxByC，，,0AxBy，，,,0λ,,0 AxByC，，,0 BxAy,，,,0λ ||AxByC，，00d,Pxy(,)6.(,AxByC，，,0). l0022AB， AxByC，，,0lAxByC:0，，,AxByC，，,0,0,0 AxByC，，AxByC，，B,0lBB .,,.l AxByC，，AxByC，，B,0lAA .,,.l ()()0AxByCAxByC，，，，,,0111222 CAxByCAxByC:()()0，，，，,()()0AxByCAxByC，，，，,,0111222111222 ()()0AxByCAxByC，，，，,111222 ()()0AxByCAxByC，，，，,111222 9. 222()()xaybr,，,, 2222xyDxEyF，，，，,0DEF，,4 xar,，cos,,,ybr,，sin,, 4 Axy(,)Bxy(,)()()()()0xxxxyyyy,,，,,,11221212 Axy(,)Bxy(,)1122 ()()()()[()()()()]0xxxxyyyyxxyyyyxx,,，,,，,,,,,,,1212112112 ,,,，,,，，，,()()()()()0xxxxyyyyaxbyc,axbyc，，,0λAB1212 22xyDxEyF，，，，,0AxByC，，,0Cl 22xyDxEyFAxByC，，，，，，，,,()0λ 2222CCxyDxEyF，，，，,0xyDxEyF，，，，,0111222122222xyDxEyFxyDxEyF，，，，，，，，，,,()0λ111222 22222Pxy(,)(x,a)，(y,b),rdaxby,,，,()()dr,,P0000 dr,,P 222(x,a)，(y,b),rAx，By，C,0d,r,相离,,,0 d,r,相切,,,0 Aa，Bb，Cd,r,相交,,,0d,22A，B OO,d12d,r，r,外离,4条公切线12 d,r，r,外切,3条公切线12 r,r,d,r，r,相交,2条公切线1212 d,r,r,内切,1条公切线12 0d,,rr,,内含,无公切线12 22xyDxEyF，，，，,0 (,)xy(,)xy0000 DxxEyy()()，，00xxyyF，，，，,00022 yykxx,,,()00 ykxb,， 222xyr，, 2xxyyr，,Pxy(,)00000 2kykxrk,,，1 ,,,(0,,)1 ,, a,b夹角,，,,[0，,]2 5 ,3l ,的夹角,，,,[0，]2 ,4lll//l=0 [0，],,,,12122 5 ,,(0,,],, 6ll ,，,,(0，,)12 ???x,x，rcos,,0(,参数),y,y，rsin,0, DE ????,,,221DE22D，E,4F??,,,222 ???? ???? x，xy，y00 ??22 22x，y，Dx，Ey，F 0000 ?? x，xy，y00 22 ?????? 22,，,????12 ??? ??? ?????? ??? 6 2222xyxy，,1，,1 2222baab ??? 22(x,m)(y,n)，,122ab 2x 2y 22xa,cos,xma,，cos,,,xya，,1 θb,,22abyb,sin,ynb,，sin,,,θ bθαtan,,tan,a 22xy22，,1cos,，sin,,122ab 2cb e,e,,12aa 2a c 2222b2xyb，,1 22caba 22xy,c，,1 kk,c 7 42222aca, 422acx, ep α1cos,e, |AF|αe 2222xyxy00Pxy(,)，,,,1(0)ab,，,1 :222200abab ,PFF 2cPFPF1212．．．．．．．．．．． ,2，FPF|PF|+|PF||PF||PF|btanS,121212,FPF．．．．．122 2222yxxy,,1,,1 2222abab ??? 22(x,m)(y,n),,122ab xa,sec,, (),为参数,yb,tan,, 2cb e,,，12aa 2a c 2222bxyxy,,0,,, ,x2222ababa 2b22y,x,,2a 8 ex,a,P在右支上,0 ,a,ex,P在左支上0,a，ex,P在右支上ey,a,P在上支上,,00,,,a,ex,P在左支上a,ey,P在下支上00,,ey，a,P在上支上,0,,ey,a,P在下支上0, 2222b2xyb,,1 ,22caba 22xy,c，,1 kk,c 2222xyxy0000,,1,1, 2222abab22,2,xybcot2,,,1(,0)ab bcoth,S,22,FPF212ab2c 22,，,12 22xy 94 ppp?222 p?pp222 ppp?222 9 p?pp222 2,x,2pt (p,0),y,2pt, 22yy 00 p ?2 p 2 p2p ?21,cos,sin, ? 2p112xx,?12，,4mnp ? 2222yyyy1212QAQB2p2p2p2p 22yyyy1212?QAQB2p2p2p ? 2222yy4pa12OA,OB224p4p Ax，By，C,0, ?,f(x,y),0, ? 直线与抛物线的对称轴平行,有唯一的公共点;, ,直线与双曲线的渐近线平行,有唯一的公共点., ΔΔ 10 Δ ,1,1,221， 1，k1，k,1，,22k,|a||a|k 22lkd,(x,x)，(y,y)2121 12d,1，y,y,d,1，kx,x21212k d,x,x,sec,d,y,y,csc,2121 x，x0(1) ??2 y，y0 2 (2) Δ (3) 22bb 22aa 1 k 11 2t4 t2t x,f(t), ,,y,(t), x,f(t), ,,y,(t), x,f(t),11,y,t,()11, 236,,,,xtxt,,,,326,,,,ytyt,, αx,x，tcos,,0,yytsin,,，0, 12 x,x，at,t，t012,y,y，bt20, x,x，rcos,,0 (,参数)???,y,y，rsin,0, 22cos,x,m，a,(x,m)(y,n)，,1 (,为参数),22absin,y,n，b, 22sec,x,m，a,(x,m)(y,n),,1 (,为参数),22ab,y,n，btg, 2,x,2pt ?(p,0),y,2pt, 1. ρθρ θρθ 2. 3. ρθ ρθ ρθρθлл ep4. ρ1,ecos, ρθ “” ,,3ρ,,22 5. y ρθρθρ???θx θαρθρθ ρρθρθ ,,x,x，hx,x,h,, ,,,,y,y，ky,y,k,, 13 pp22ypxPFxypxPFx,,，,,,,，2:;2:1122 22pp11xpyPFyxpyPFy,,，,,,,，2:;2:22 2ypxp,,2(0)Pxy(,)00 2,,,ypxp2(0) 112222AB,1，k,x,x,(1，k)[(x，x),4xx],1，,y,y,(1，),[(y，y),4yy]21121221121222kk2y=2px(p>0) 22p1x+x+p;2yy=pxx=; AB1212124 22xya>b>0AB AB,2a，e(x，x)，,11222ab 22xy，,122ab 222bxxy0Pxy(,)Pxy(,),,1k=2200002abay0 2bx20ypxp,,2(0)Pxy(,)k=002ay0 pk= y0 ,,0 (2) 22b a 2b2ppc 22xy，,122ab ,a，,a,bλ,1，,1，, ?? λλ??PO,OQ, λ?λ??)=10,-10+2x+3y=0. 14 ? 222yyy?Δ111 5324,x,124 22x，y 2y6.??2 346 22 7.a?x?+y?=a?(o