algebra b lykeiou

1. 001-126_update.indd 1 10/5/2013 8:48:43

2. : . . : 1991 : 1992, 1993, 1994, 1995, 1996, 1997, 1998, 2012 . & , - / & / . . 001-126_update.indd 2 21/2/2014 4:36:43

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4. 001-126_update.indd 4 10/5/2013 8:48:43

5. . (2010) , - . , . , . , . . . : , (2010), . , . , . , . . . (2010), - (2010). : 1 , - , . , . 2 , , , . 3 - . , , - . - . 4 - - . 5 , . 001-126_update.indd 5 10/5/2013 8:48:43

6. 001-126_update.indd 6 10/5/2013 8:48:43

7. 1 : 1.1 .........................................................................9 1.2 .................................................................24 2 : 2.1 -- ...............................30 2.2 - ..............................40 3 : 3.1 .....................................................49 3.2 .............................................60 3.3 1 .........................................................65 3.4 .....................................................73 3.5 ...............................................83 3.6 ..............................89 3.7 2..........................................97 3.8 .....................103 3.9 f(x)=x+x.....................................................108 3.10 ..........................................................................114 4 : - 4.1 .....................................................................................128 4.2 ...................................................................132 4.3 ........................................140 4.4 ..........150 5 : 5.1 ......................................................................160 5.2 ......................................................................................173 5.3 ................................................................181 .................................................................193 - .............................195 001-126_update.indd 7 10/5/2013 8:48:43

8. 001-126_update.indd 8 10/5/2013 8:48:43

9. 1 1.1 x + y = x + y = , 0 0, , . : : 0, : x y y x y x + = = + = + , - = y'y . : 9 0, (. ), x+y=, =0 O x y x+y=, 0 x y O 001-126_update.indd 9 10/5/2013 8:48:44

10. 10 1 : 9 = 0 , y = x'x y'y (. ). = 0 ( 0), . - y'y x'x . : 9 x y =2 2 = 1 2 y'y 1. 9 y = 2 x'x - y'y 2 . 9 x = 2 y'y - x'x 2. . y x= 1 2 1 x x= = 001-126_update.indd 10 10/5/2013 8:48:44

11. 1.1 11 , (4, 1) x y =2 6, 4 2 1 4 2 6 = + =( ) . , , (16,5), ( , ) 10 8 . 2 x 2 x+y= x+y= , , , 2 x 2 x y x y + = + = ' ' ' . . - . . : . () (') , .. (), + ( ) ' ( ') , () - 0, (') '. + ( ) ' ( ') () ('). - 2o : 9 0, : = = 9 = = , + = +. , , : x y x y = + = 2 6 1 3 4 8 2 ( ) ( ) 001-126_update.indd 11 10/5/2013 8:48:45

12. 12 1 : , ( ) , .. (1) x. x 3 2 6 4 8 6 18 4 8 10 10 1 ( )y y y y y y + + = + + = = = y : x = + =2 1 6 4( ) ( , ).4 1 , . - , . , x = 4 y = 1, : 1 : 4 2(1) = 6 2 : 3 4 4 1 12 4 8 + = =( ) ( ) , : x y x y = + + = 2 6 3 4 8 x y y = + = 2 6 1 001-126_update.indd 12 10/5/2013 8:48:46

13. 1.1 13 , , : . : x x x = + = =2 1 6 2 6 4( ) . ( , )4 1 ( - ). 2 x 2 . , - . , , , . 2 x 2 . , 2 x 2 , , , . + = + = 3 6 18 3 4 8 x y x y x y x y = + = 2 6 3 4 8 + + + = + = = 3 6 3 4 18 8 10 10 1x y x y y y x y x y = + = 2 6 3 4 8 x y x y + = + = ' ' ' A(4, 1) 3x+4y=8 x2y=6 y O x . (3) . 1 001-126_update.indd 13 10/5/2013 8:48:47

14. 14 1 : 2 x 2 . : 9 2 3 3 4 9 1 x y x y + = = y x y x = + = 2 3 1 4 9 1 9 , , . , (1, 0,3) . , - 1 1 3 , . 9 x y x y + = + = 2 3 2 4 5 y x y x = + = 1 2 3 2 1 2 5 4 , , . 9 y x x y + = = 1 2 4 2 2 y x y x = = 2 1 2 1 , . . y x 21 1 1 O y x 1 2 O x y 2 1 O, 001-126_update.indd 14 10/5/2013 8:48:48

15. 1.1 15 , 2 x 2 : 9 9 9 . 2 x 2 - 2 x 2 . 0 0. - : 1 2 1 = 2 = ' ' . ' ' , ' ' 0 , 1 2 , + = + = = ' ' ' ' ' ' ' ' ( ' ' ) ' x x x x ' ' ' ' ' = x : x y x y + = + = ' ' ' y x y x = + = + ( ) ' ' ' ' ( ) 1 2 y = + = + + ' ' ' ' ' ' ' ' ( ' ' ) ( ' ' ) ( ' ' ) = 001-126_update.indd 15 10/5/2013 8:48:49

16. 16 1 : y = ' ' ' ' , , = ' ' , =0 , 1 2 , . . =0 ' =0. : ' ' 0 ' ' = 0 . ' ' , : . D, x , : . , D, y , : . ( , ) ' ' ' ' , ' ' ' ' x y = x y x y + = + = ' ' ' ( , ) ' ' ' ' , ' ' ' ' x y = D = ' ' D = = ' ' ' ' Dy = = ' ' ' ' 001-126_update.indd 16 10/5/2013 8:48:50

17. 1.1 17 , , : : 9 , . : . , ( , ) ( , )x y = 4 1 . 9 . 2, 2 3 40x y = . . x y x y = + = 2 6 3 4 8 D = = = + = 1 3 4 2 1 4 3 2 4 6 10 0( ) Dx = = + = 6 8 4 2 24 16 40 y D D y = = = 10 10 1x D D x = = = 40 10 4 2 3 40 2 40 3 x y y x = = D0, , (x,y) D=0, . x y x y + = + = ' ' ' y D D y = 2 3 40 4 6 80 x y x y = = 2 3 40 2 3 40 x y x y = = , x D D x = 001-126_update.indd 17 10/5/2013 8:48:51

18. 18 1 : 9 . . 1 - , . , . , . , . D, Dx, Dy. : k k k, , 2 40 3 3 11 9 3 6 x y x y + = + = 3 11 3 2 x y x y + = + = x y x y = = 1 22 D D D x y = = + = = = + = = 1 11 2 2 2 2 2 1 2 1 2 2 2 ( ) ( ) == = + = 2 2 2 2 1 1 1 2( ) ( ) ( ) 001-126_update.indd 18 10/5/2013 8:48:52

19. 1.1 19 , D = 0 . : : 9 D 0, 0 2, (x, y), : . , 0 2 , . 9 D = 0 , = 0 = 2 , . : = 0 , . = 2 , . , , 3 x 3 x+y+z=0 , - , , , . . 2x+3y+z=6 - ( , , )2 1 5 , 22+3(1)+5=6. D = = = =0 2 0 0 2 ( ) x D D x = = = = 2 2 2 2 1 ( ) ( ) ( ) y D D y = = = = 2 2 2 2 2 2 ( ) ( ) ( ) ( ) 0 1 0 2 0 1 0 x y x y y y = = = = 2 1 4 2 2 2 1 2 1 x y x y x y x y = = = = . 1 , 2 1 2 1x y y x = = 001-126_update.indd 19 7/5/2014 4:36:51

20. 20 1 : : 1 1 1 1x y z+ + = , 2 2 2 2x y z+ + = 3 3 3 3x y z+ + = , - , , 3 x 3 - 2 x 2 . . , .. (3) z, - . : (4) (1) (2) : 9 2 3 9 2 3 3 8 9 11 2 15x y z x y x y x y + = + + = + =( ) (5) 9 (6) (5), (6) x=1 y=2 . x y (4) z = 3. ( , , ).1 2 3 x y z x y x y x y+ = + + = + =3 10 3 3 8 10 1( ) 1 1 1 1 2 2 2 2 3 3 3 3 x y z x y z x y z + + = + + = + + = 2 3 3 10 2 3 8 3 x y z x y z x y z + = + = + = ( ) ( ) 3 8 3 8x y z z x y+ = = + 3 x 3, , 2 x 2, 3 x 3 . 11 2 15 1 x y x y + = + = , 001-126_update.indd 20 10/5/2013 8:48:54

21. 1.1 21 1. i) ii) . 2. i) ii) 3. : i) ii) 4. : i) ii) 5. : i) ii) 6. , . i) ii) iii) 7. : i)ii) x y x y 7 8 45 = + = x y x y = = 3 3 3 2 2 2 1 2 1 0 y x x y = + + = 2 7 3 5 4 x y x y + = = 2 5 4 6 7 100 x y x y = + = ( ) ( ) 3 1 4 7 1 2 3 1 1 + + = + = x y x y 2 3 40 4 6 80 x y x y = = x y x y = + = 1 3 2 4 4 3 8 x y x y + + + = + = 5 2 2 1 7 2 0 6 3 6 2 8 2 3 8 3 1 0 y x x y = + + = x y x y = + = 4 2 ( ) ( ) 3 1 2 2 3 1 1 3 + = + + = x y x y 3 11 9 3 2 x y x y + = = 2 1 3 4 2 4 3 2 3 3 x y x x y = + + = 001-126_update.indd 21 10/5/2013 8:48:55

22. 22 1 : 8. : i) ii) iii) 1. i) 1 2 . ii) 1 2 ; 2. 26 , 68 . ; 3. 1,5 4. 2200 - 5050 . . 4. R T R =T + . 20 C 0,4 80 C 0,5 , . 5. , 50% - 80% . 100 ml 68% ; 6. 1 2 4 3: x y+ = 2 2: x y+ = , . i) 1 2 . ii) - ; iii) ; 3 2 11 2 5 2 3 5 2 33 x y x y x y = = + = 5 3 4 3 2 3 2 2 2 x y x y x y + = + = + = x y x y x y + = + + = + = 2 2 3 3 2 5 5 3 2 16 y x1 4 1 1 2 2 O 001-126_update.indd 22 10/5/2013 8:48:56

23. 1.1 23 7. : i) 1 2 : x y+ = 2 1: x y+ = . ii) 3 : x y = 4 1: x y+ = . 8. : i) ii) 9. 1 2 6= , O O1 3 5= O O2 3 7= . . 10. , . N = x , B = y = z , - , . 11. . 50% , 10% 30% . 52 lit 32% , - . . 12. - , y x x= + + 2 . . ( ) ( ) , = + = 1 2 1 4 1 2 x y x y ( ) ( ) , + = + + = 2 5 5 2 5 x y x y 1 2 3 y x1 K(1,4) y=g(x) O y x y=h(x) O 2 4 4 y x y=f(x) O K(2, 1) 3 001-126_update.indd 23 10/5/2013 8:48:58

24. 24 1 : 1.2 , - . , 13 89. x, y , x y+ =13 x y2 2 89+ = . , : : (1), , .. x , (2). x y y x+ = = 13 13 (3). 2 = 9 . : (3), x=8 y=5 , x=5 y=8. (8, 5) (5, 8). 5 8. , , . 1o x y x y + = + = 13 89 22 2 ( ) x x x x x x x x x 2 2 2 2 2 2 13 89 169 26 89 2 26 80 0 13 40 0 + = + + = + = + = ( ) . x = 13 3 2 8 5 001-126_update.indd 24 10/5/2013 8:48:59

25. (1) x (2). : (3) x=2 y=3 , x=3 y=2 . (2, 3) (3, 2) . - 5 6. , - Vieta 2 5 6 0 + = . 2 3 (2,3) (3,2). x+y=5 , xy = 6 y x = 6 . - . x y y x+ = = 5 5 y xO 1 1 A B (3). xy x x x x x x = = = + = 6 5 6 5 6 5 6 0 2 2 ( ) =x 2 x = 3. 1.2 25 001-126_update.indd 25 7/5/2014 4:37:35

26. 26 1 : (2,3) (3,2) . (2,3) (3,2) . 2 (1) x (2). (2) : . x2 = , 2 13 36 0 + = , =9 =4 . 9 =9 x 2 = 9 x = 3 x = 3 (1) x=3 y=2 x = 3 y = 2 . 9 = 4 . (1) x=2 y=3 x = 2 y = 3. (3,2), ( , ), 3 2 (2,3) ( , ). 2 3 xy = 6 y x = 6 , - x y2 2 13+ = (0,0) = 13 . xy y x = =6 6 x y x x x x x x x x 2 2 2 2 2 2 4 2 4 2 13 6 13 36 13 36 13 13 36 + = + = + = + = + = 00 x x2 4 2= = x = 2 xy x y = + = 6 1 13 22 2 ( ) ( ) 001-126_update.indd 26 10/5/2013 8:49:01

27. 1.2 27 1. : 2. : i) ii) iii) . 3. S t t= + 0 21 2 = +0 t , S t= + 0 2 . 1. o - . x y xy x y 2 2 3 1 + + = + = . y x x y = = 3 12 3 4 2 x y x y 2 2 9 0 + = = x y xy 2 2 5 2 + = = . x y x y 2 2 2 2 10 25 = + + = y x 1 A B A B 001-126_update.indd 27 10/5/2013 8:49:02

28. 28 1 : 2. : 3. 120cm 2 . - 3cm , 2cm , - . . 4. y x= 2 y x= + . k . 5. o 2 2 y x y x = = + . 1 I. : , , , , , . ) , ) , ) . II. , , . 1. , . A 2. D = 0 , . 3. xy x y = + = 1 0 . 4. x y2 2 1+ = y x= +2 1 . A ( ):1 2 1 2 4 0 x y x y + = + = ( ):2 1 2 4 x y x y + = + = ( ):3 2 4 2 2 1 x y x y + = + = ( ):4 2 1 1 x y x y = + = (1 ) (2 ) (3 ) (4 ) 2 5 0 4 3 2 2 xy y y y x x = = + 001-126_update.indd 28 10/5/2013 8:49:03

29. 001-126_update.indd 29 10/5/2013 8:49:03

30. 2 ) [4,16] . . . 2.1 -- T = f (t) t (t =0) (t =24). T=f(t) 5 11 T(C) 3 4 16 24 t(h) f(t1) T=f(t) f(t2) 5 11 T(C) 4 t 16 24 t(h)1 t2 001-126_update.indd 30 10/5/2013 8:49:03

31. 2.1 -- 31 , , - , t t1 2 4 16, [ , ] t t1 2< : f t f t( ) ( )1 2< T = f (t ) [4,16] . : f f . , f x x( ) = 2 3 . , x x1 2< . : : f x x( ) = + , > 0 . ) , [16,24] . f , x x1 2, x x1 2< : f x f x( ) ( )1 2< x x R1 2, T=f(t) 5 T(C) 4 16 t1 t2 24 t(h) f(t )1 f(t )2 x x x x x x f x f x 1 2 1 2 1 2 1 2 2 2 2 3 2 3 < < < x x x x x x f x f x 1 2 1 2 1 2 1 2 2 2 2 5 2 5 < > + > + >( ) ( ) f , x x1 2, x x1 2< : f (x1 ) > f (x2 ) T=f(t) 5 11 T(C) 3 O 4 16 24 t(h) 001-126_update.indd 32 10/5/2013 8:49:05

33. 2.1 -- 33 : ) t1 4= , f ( )4 3= . : f t f( ) ( ) =4 3 , t[ , ]0 24 T = f (t) t = 4 , f ( )4 3= . : x A0 , f x( )0 f min f (x) . , f x x( ) = +3 14 . x4 0 , x, 3 04 x , x, 3 1 14 x + , x. : f x f( ) ( ) 0 , x. , f x0 0= , f ( )0 1= ) t2 16= , T(16)=11 . : f t f( ) ( ) =16 11 , t[ , ]0 24 T = f (t) t =16 , f (16)=11. : f, , x A0 () : f x f x( ) ( ) 0 , x A f, , x A0 () : f x f x( ) ( ) 0 , x A 001-126_update.indd 33 10/5/2013 8:49:08

34. 34 2 : x A0 , f x( )0 - f max f ( x) . , f x x( ) = +3 14 . x4 0 , x, 3 04 x , x, + 3 1 14 x , x. : f x f( ) ( ) 0 , x , f x0 0= , f ( )0 1= . () () . (. ) (. ) (. ) (. ). x y 1 1 y=f(x) y x 1 11 y=f(x) y x 1 y=f(x) 1 y x 1 1 y=f(x) 001-126_update.indd 34 10/5/2013 8:49:09

35. 2.1 -- 35 ) - Cf f . Cf y'y, - Cf y'y Cf . , , M(x, y) Cf y'y M x y'( , ) M(x, y) M x y'( , ) Cf , y = f (x) y = f ( x), : f . : yy. , f x x x( ) = +2 14 2 , x : f x x x x x f x( ) ( ) ( ) ( ) = + = + =2 1 2 14 2 4 2 , y'y. ) - Cf f . Cf , - Cf - Cf . f, , , x A : x A f x f x( ) ( ) = f x f x( ) ( ) = y xx y x M M O f(x) f(x) Cf y y y xx x M M O f(x) f(x) Cf 001-126_update.indd 35 10/5/2013 8:49:10

36. 36 2 : , , M(x, y) Cf M x y'( , ) M(x, y) M x y'( , ) Cf , y = f ( x) = y f x( ), : f x f x( ) ( ) = f . : . , f x x x( ) = 2 3 , x : f x x x x x f x( ) ( ) ( ) ( ) = = + = 2 23 3 , . : y x= 2 , y x= 4 , y x= 6 ., , y'y , , y x= , y x= 3 , y x= 5 ., , , . - f [6,6]. f : ) f : f, , , x A : x A f x f x( ) ( ) = 001-126_update.indd 36 10/5/2013 8:49:11

37. 2.1 -- 37 i) , ii) , iii) . ) f , - . f , y'y . , y'y f, - f, (). : ) f : i) [0,2] [5,6], ii) [ , ]2 0 [ , ], 6 5 [0,2] [5,6] f . iii) [ , ] 5 2 [2,5] . y x 1 4 652256 x A A B 001-126_update.indd 37 10/5/2013 8:49:12

38. 38 2 : ) f 4 x 6 6. : max ( ) ( ) ( )f x f f= = =6 6 4 f 0 x 0. : min f (x) = f (0) = 0. 1) - : ) ) . 2) - , . 3) : i) f x x x( ) = +2 6 10 x=3. ii) g x x x ( ) = + 2 12 x=1. 4) : i) f x x x1 2 4 3 5( ) = + ii) f x x2 3 1( ) = + iii) f x x3 1( ) = + iv) f x x x4 3 5 3( ) = v) f x x x 5 2 1 ( ) = + vi) f x x x 6 2 2 1 ( ) = + . 1 1 y=f(x) x y 2 2 y=g(x) x y 1 y=h(x) x y 1 2 001-126_update.indd 38 10/5/2013 8:49:14

39. 2.1 -- 39 5) : i) f x x 1 1 ( ) = ii) f x x2 2( ) = iii) f x x x3 1 1( ) = + iv) f x x x x 4 2 1 1 ( ) = + + v) f x x5 ( ) = vi) f x x6 2 1( ) = . 6) . 7) 8) - ) ) . y=f(x) y=g(x) y=h(x) x x x y y y y=f(x) y=g(x) y=h(x) x x x y y y C C C x x x y y y 1 32 001-126_update.indd 39 10/5/2013 8:49:15

40. 40 2 : 2.2 - ) f x x( ) = +1 . f x x x x x ( ) , , ,= ++ 1 0 1 0 - f x x( ) = +1 , - 9 y x= +1, x 0 9 y x= +1, x 0 , 1 y'y x Oy' xOy , , ( )x x= (). , ( )x x= - (1) 1 , f x x( ) = +1. , , , : f x x( ) ( )= + 1 , x, x f (x) 1 (x) . : (1) y'y . f , : f x x c( ) ( )= + , c0 , c ( ) y y=|x|+1 y=|x| 1 1 1 1 1 1 O xx' 001-126_update.indd 40 10/5/2013 8:49:16

41. 2.2 - 41 ) f x x( ) = 1 . f x x( ) = 1 , 9 y x= 1 , x 0 9 y x= 1, x 0 , 1 y'y - x Oy' xy ( )x x= (). , ( )x x= - 1 , f x x( ) = 1 . , , , : f x x( ) ( )= 1 , x, x f (x) 1 (x). : f , : f x x c( ) ( )= , c0 , c ( ) y y=|x|1 y=|x| 1 1 1 1 1 1 O x x c y=(x) y=(x)+c c cc y c O f x x x x x ( ) , , ,= 1 0 1 0 001-126_update.indd 41 10/5/2013 8:49:18

42. 42 2 : ) f x x( ) = 1 . f x x x x x ( ) , , ,= + 1 1 1 1 f x x( ) = 1 , 9 y x= +1, x 1 9 y x= 1, x 1, 1 x'x - x Oy' xOy ( )x x= (). , ( )x x= (2) 1 , - f x x( ) = 1 . , , , f x x( ) ( )= 1 , x, f x x( ) = 1 x ( )x x= x 1. (2) x'x . x y=(x) y=(x)c y c c cc c O y x y=|x|1 y=|x| 1 1 1 1 1 O 001-126_update.indd 42 10/5/2013 8:49:19

43. 2.2 - 43 f : f x x c( ) ( )= , c0 , c ( ). : f x x c( ) ( )= , f x x c, c x. , f c ( ). ) f x x( ) = +1 . f x x( ) = +1 9 y x= 1 , x 1 9 y x= +1 , x 1 , 1 x'x - x Oy' xOy ( )x x= (). , ( )x x= 1 , Ox c c c c xxc (x-c) C C f(x) y f y x y=|x+1| y=|x| 1 1 11 11 O 001-126_update.indd 43 10/5/2013 8:49:20

44. 44 2 : f , : f x x c( ) ( )= + , c0 , c ( ). f x x( ) = +1 . , , , f x x( ) ( )= + 1 , x, f x x( ) = +1 x ( )x x= x +1. : f x x c( ) ( )= + , f x x + c , c x. , f c ( ). f x x( ) = + +3 2 . y x= + 3 , - y x= 3 . y x= + +3 2 , - y x= + 3 2 . xx x+c yc c O c c =(x+c)f(x) C Cf 001-126_update.indd 44 10/5/2013 8:49:21

45. 2.2 - 45 , - f x x( ) = + +3 2 - - y x= , - 3 - 2 (). : , - : f x x c d( ) ( )= , c,d0 , . A 1. - : ( )x x= , f x x( ) = + 2 g x x( ) = 2 . 2. : ( )x x= , h x x( ) = + 2 q x x( ) = 2 . 3. : ( )x x= , F x x( ) = + +2 1 G x x( ) = 2 1 . y x y=|x+3|y=|x+3|+2 y=|x| 13 2 O 001-126_update.indd 45 10/5/2013 8:49:23

46. 46 2 : 4. i) f x x x( ) = +2 4 52 f x x p q( ) ( )= + 2 - g x x( ) = 2 2 f. ii) f x x x( ) = + 2 8 92 , - g g x x( ) = 2 2 . 5. 1 O(0,0) A(2,0). - : i) f x x( ) ( )= + 2 g x x( ) ( )= 2 ii) h x x( ) ( )= + 3 q x x( ) ( )= 3 iii) F x x( ) ( )= + + 3 2 G x x( ) ( )= 3 2 . 6. ( )x x= 2 12 . - f : i) 2 1 . ii) 3 2 . iii) 2 1 . iv) 3 2 . C O x y 001-126_update.indd 46 10/5/2013 8:49:24

47. 2.2 - 47 I) - , , - . 1. f , f . 2. . 3. (1,2) , (2,1) (3,3) . 4. f 1, f (0)0 . 5. f - (1,2) (2,5) , f . 6. f 1, f (x) = 2 . 7. f :[ , ] 1 2 f x x( ) = 3 2 . 8. , . 9. f , f - . 10. f , f . II) f. f, ( )x x= 3 4 , 1 2 , : ) f x x( ) ( )= +3 1 24 ) f x x( ) ( )= 3 1 24 ) f x x( ) ( )= + +3 1 24 ) f x x( ) ( )= + 3 1 24 2 001-126_update.indd 47 10/5/2013 8:49:25

48. 001-126_update.indd 48 10/5/2013 8:49:25

49. . - MM1 NN1 , OMM1 ON N 1 , : , , , 3 ( ) ( ) ( ) ( ) MM OM NN ON 1 1 = ( ) ( ) ( ) ( ) OM OM ON ON 1 1 = ( ) ( ) ( ) ( ) MM OM NN ON 1 1 1 1 = 3.1 ( ) ( ) MM OM 1 ( ) ( ) OM OM 1 ( ) ( ) MM OM 1 1 , - . , , - , , , . , M OM1 , : = ( ) ( ) MM OM 1 11 ( ) 001-126_update.indd 49 10/5/2013 8:49:26

50. 50 3 : , - , , 0 360 Oxy , Ot Ox - Ot (. , ). Ox , Ot . (x, y) M1 x'x (. ). (. ), , , : , , ( )1 = x , ( )1M y= ( )OM x y= + = 2 2 0 . , : , , , . = ( ) ( ) MM OM 1 = ( ) ( ) M OM 1 = ( ) ( ) MM OM 1 1 = ( ) ( ) M M 1 1 = y = x = y x = x y = + x y2 2 0 = ( ) ( ) M OM 1 = ( ) ( ) MM OM 1 1 = ( ) ( ) M M 1 1 2 1 1 2 x xx t y t (x,y) (x,y) yy ( ) ( ) ( ) 001-126_update.indd 50 10/5/2013 8:49:28

51. 3.1 51 , - ( ). : (x, y) ( ) = + x y2 2 0 . 360 Ox - Oxy - . 30 , Ox = + =360 30 390 . 360 , - : = +360 , N * 0 o 360 o Ox, , - - 30 , Ox 360 + 30 = 390 : , ( x0) , , ( y0) = y = y x = x = x y = + x y2 2 0 = + = ( )360 30 390 y x 390 30 0 0 0 y t t x 30 390 0 001-126_update.indd 51 10/5/2013 8:49:29

52. 52 3 : : = +( ),360 N 0 360 360 o , , 0 360 . , , , : (x, y) ( ) = + x y2 2 0 . ( ) Ox . Ox , , - , +360 , . Ox , , , + 360 , - . , k +360 , k , . , k : , = y = y x = x = x y = + x y2 2 0 ( ) ,k + =360 ( )k + =360 ( ) ,k + =360 ( )k + =360 ( x0) , ( y0) , 001-126_update.indd 52 10/5/2013 8:49:30

53. 3.1 53 (0,0) - = 1 - . - . - , .. - = 35 , (, ). 35 = =1 35 0 57= , . , , , . - , . , 35 = =1, 35 0 82= , . , - (x, y), : x'x , y'y . : 1. , 1. : = x = = y = 1 1 1 1 70 60 50 40 20 30 10 1 350 340 330 320 310 300 290 280270260 250 240 220 230 210 200 190 180 170 160 150 140 130 120 110 100 90 80 y x (x,y) N(,) x y 35 0,1 0,1 0 o o o o o o o o o o o o ooo o o o o o o o o o o o o o o o o o o o o 001-126_update.indd 53 10/5/2013 8:49:31

54. 54 3 : 2. , , . + + + + + + + + - M(x, y). - . 1 , yE , (AE)= yE , = yE. . : = yE = , x = 1 , - . A O B B M A t x y E(1,y )E 1 2 3 4 = = = ( ) ( ) ( ) ( ) 1 001-126_update.indd 54 10/5/2013 8:49:32

55. 3.1 55 . , AB (, ) ( 1rad), . , ( rad) S = . - : ( 1 rad ) , , ( 1 rad). - , : rad . - 2, 360 2 rad. , 1 rad 360 2 , , rad 180 . , = 180 , : : 9 60 , = 60 = = 60 180 3 60 3 = rad. A 1rad B O 001-126_update.indd 55 7/5/2014 4:40:07

algebra b lykeiou

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