NJJ00002zw2.PDF

Transcription

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6 m + t si / cos (m ) m

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9 si A cosa + = m cosa sia si A + cos A = m siacosa m sia siacosa sia cosa m f cos si 5 (si ) si 5 si fm f mi fmi si f mi

10 y = y = y y = k y y k + + = ( )

11 PQ k

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13 C A B C C C A B B A C C C B A B B B A A A

14 S q q ( )

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19 y 5

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21 0] f(. 5) b f( ) c f() b c f( ) f( ) f() f(. 5) f(. 5) f() f(. 5) f( ) AM P BM P D M P P (B)

22 g() log 0 m0 m 0 0 m m(m ) 0

23 D e y ( ) 0 y y 9 y ( ) y A

24 B C D y P( y) PO (O ) P( y) ( ) y OP log ( + )

25 log log ( ) log log ( ) + + A f( ) f( 5 ) f() B f() f( 5 ) f( ) Cf() f( ) f( 5 ) Df( 5 ) f() f( )

26 b 0 b log b y log b z ( + b ) b logb log logb0 = + = log (b) log (b) b b b + b b b

27 6 A { k k Z} B { } A{ } B { } 5 C{ 5 } tcos y tsi t 0 0 k (k Z)

28 B D B D t f( t) f( t) (B) + b

29 b 0] [0 ] 0 [0 ] [0 ] 0 b ( )

30 C D (D)

31 7 m ( ) (*) ( ) 7 m ( )

32 H A A

33 bi = ( bi)(cos + si ) ( ) ( i) y 0 0 C D y ( ) f() ( 0) y f ()

34 y ( 0) (y) 0 0 y y 86 f () f () = cos( ) f () = rcsi f () π N {( y) y } M N A ( ) M N y +

35 cos y + cos si =

36 5 y t( ) ( 6) ( ) k k k k 5 k k k 0 5 A

37 0 ( )[( ) ] 0 f( ) f( ) 0 (0) 0 (0) A B f() f( ) ( ) 0

38

39 f( ) f( ) ( 0 ) f( ) f() f() y ( ) [ ) m m m m 7 ( ) (*) ( ) 7 m ( )

40 t p f(t) 0 Pmi 0 ( log ) log 0 ( log ) (0 ) (8 ) 8 y 7 7 u v v (u )(uv 7 )0 v (u )(v 0) 0 ( 7 0) u y y [ 7 )

41 9 y log [si( )] si( ) 0 k k k k y f() k 6 5 k k k (k ) 6 (k 5 k ] k 6 50 f() [ ]( ) f( ) f() ( ) f() f( ) ( ) ( ) f() f( ) f( ) f() ( ) ( ) ( ) f() 5 f() l

42 y l y l( ) ( 0) ( ) 0 f() 0

43 ( 0) g() [f() f( )] h() [f() f( ) 0 g() [f() f( )] 0 0 lg lg g() h() lg(0 ) 57 y 6 ( ) ( 6 ) 7 7 si 6 7cos [0 ] y 7si 7cos 5si( ψ)

44 [ 5 5 t ϕ ϕ ϕ ϕ si( ϕ) ] y [ 7 5] 8 5 y = ( 0) cos si( ) y [ ] (k) k 0 0 ( k) k 0 k 0 0 ( k 0 k ) k 60 y y ( ) ( ) [ ] ( ) ( ( ) ) ( ) cos [ ] y si cos si( )

45 si( ) y [ ] 6 f() f( ) f( ) f() f( ) f( ) f( ) y y f( ) y f() y f() k k 0 ( 0) k

46 m / / y f(0) 0 f() 0 65 y 0 y ( ) ( ) y p p y p y y y y y y [ ] y m 66 0 m y 0 P AB P( y) AP y ( 0) PB

47 0 m m m 5( 0 ) 0 ()0 m 0 m 0 () () m m 0 k k 0 k k k ( bi)( bi) b k k 0 k l k ( ) k ( ) f() ( ) f() ( ) 8 0 ( 0 ) ( )( ) 0 0

48 0 0 ( )( ) ( ) / ( ) [( ) 7( ) 0] / ( ) ( ) 0 / ( ) (0 7 0 ] 9 yz y z yz f() log f() f() f( ) log ( ) l og ( ) 0 f() ( ) 7 7 f() [ ] y g() f() f( ) 8 9 f() f() 8 9 9

49 f( ) 7 7 f() f( ) 8 7 [ 7 ] g() f() 8 8 f( ) 7 g() t ( f( ) t) 7 y (t ) t y y t y y y g() [ ] y 7 u y 7 u ( ) u u y 7 u u y 7 7 u y 7 0 y 0 y 7 (0 ) ( ) y u v ( ] y ( ] y y ( ] 7 77 y ( ) [ ] 7 y 7 7

50 ( 7 ) 9 8 [ 7 ] 5 78 y l og ( 0) 5 y y log y y [ 0] y mi l og 8 5 y log 9 m [ ] 8 79 y y 8y 0 y y 0 [ ] 80 y ( 0 ) f () log ( 0 ) 0 ( ) ( ) m ( m ) 9m m m 0 m 0

51 8 y t(t 0) 7 y t t (t ) log ( ) { 5 5 } f(0) f( ) [0 ] f() 0 f() f( ) cossi f( ) f() f( ) f( ) cos( ) si ( ) f() coscos( ) cos cos ( ) ( ) [ ]

52 f() ( )si( ) () [0 ] si( ) [ ] ( ) f() ( ) ( ) (ii) f() ( ) [ ] f( ) () f() () f () f ( ) () f() f( ) f( ) f( ) f( ) f( ) f( ) [ ] f()

53 f ()f ( ) f ( ) f () (*) (*) 86 ( )(y y ) y 0 f() f( y) y y y y f( y) log ( ) 0 log ( ) log ( ) 0 log ( )

54 { } 88 y f() t t (t 0) f() 0 () f() ( t t ) f() 0 ( t t ) 0 b + (t ) b (t ) + [(t ) ] t b t [ (t ) ] t

55 ( 5 ) ( 5 ) f() ( 5 ) ( 5 ) f() () c f( c ) 0 f( c) f c c () (c 0) y c c f( c) f() f( ) f( ) c f( ) 0 f( c) f() c y (c 0) c c f(c) f(0) f( )f( ) c f(0) f( ) 0 9 f() 0

56 ( ) 0 0 { 0 } f( ) f( ) ( ) (i) ( ) ( )( ) 0 (ii) 0 [ 0 ) 0 9 b y b( 0) b y y ( b ) b 0 b

57 A ( ) B ( ) C (0 ) ( ) D (0 ) ( ) ()f() log ( ) log ( ) f () log ( ) ( ) ( ) u ( ) ( )(*) 0 0 (*) ( ) 0 ( ) (*) 0 { ( ) } m 6 ( ) 0 log 0 log y y log y 5

58 y y M( ) y 95 y y y [(y) ( y )]

59 [ ] (y) mi ( ) ( ) (6 )

60 b ()A B b ( 5) b ( d 5) ( ) 0 b log ( ) ( ) log log log ( ) ( ) log (+) log(+) 00 Z log ( ) l og ( ) A Z A {} 5 log ( ) log ( ) [ ) 0 u v log u log v = log (u ) log (v )( )

61 t t m = y = t A B t t mi = 0 yy y 0 0 y 0

62 = f() = [ b] [ f() = b = f(b) = b b = b (b) = 0 b = + b = 0 = + b = b =

63 f() = b f(b) = b = 7 = 7 b = 7 b b 0 () b0 0 [f() f(0)] b f() = f(0) = b = b = = 7 b = 0 f( b) = () b0 [f(b) f(0)] ( ) f( 0) = b b

64 b = 0 9 = 6 = = 7 b = b = [0 ] f() = + + ( ) ( ) = 7 = = f() ( ) f() 7 7 [0 ] = 0 = f() 0 [0 ] 0 = ( )( ) = ( )[( ) ( )] = ( )[ ( ) + ( + )] 0 0 [0 ] f() = ( + ) 0 t = ( )

65 f() f() f() f() f() f() ( ) = f() f() f() t t f( ) f( )

66 t t t t t t t 0 t = (t t ) t t f( ) f( ) [0 ] f( ) f( ) 5 b b { b b b + b + ( ) = ( ) () 0 = ( ) 0 0 b 5 () = ( ) b + b + c f() = log [0 ] +

67 () log 7 5 f( ) log () y = f() = + b + c y y ( ) b + ( y c) = 0 + c = + 8c b = b = b = c = c = ( ) ( ) = b = f( ) f( 6 6 ) f( ) f( ) = log 7 f( 5 ) = log 5 b = f( ) f( ) f( ) 6 6 f( 7 ) = log f( ) = log log f( ) log ] f() 6b = b = y = f() =

68 f() [ ] y = y y = 0 = ( y ) ( y ) 0 y y [ ] f() ()f() g() = log ( ) 0 0 log ( ) 0 f( ) g( ) log ( ) 0 f() g() = = log ( ) = 0 f() = g() log ( ) 0 f() g() g() = log = =

69 yzcos0 = ( ) z zcos0 = ( ) = ABC C = 90 AC = BC = ysi0 yzsi0zsi0 = y z z y = + + y z y z y z y z z y + + = + + y z y z

70 m = + + = + p q r p q / 8 = 0 qr / 8 = 0 rp / 8 = 0 = p q r p q r = (p q r) / 0 y z = y z = y z =

71 = ( )( ) = ( )[( ) ( ) ] 0 7 f() [ ] y = g() = f() f( ) 8 9 f() f() f( ) t = f() y = (t ) ( t ) [ ] y t = y = 7 mi 9 t = y = 7 m y = g() [ ] = 0 [ 7] f() = + g() = 7 F() = [ 7] 0 y = log ( ) u = y = log ( ) y = log u =

72 = ( ) + 9 (0 ) u = (0 ] [ ) y = log u (0 ) y = log ( ) (0 ] [ ) f() = lg( + ) f( ) = lg( + ) = lg( + ) ( + )( + + ) = + = ( + + ) f( ) = lg( + + ) = lg( + + ) = f() f() = lg( + ) ( ) ( ) 0

73 b f( ) f() b ( ) f( ) = b 6 0 b u u b = ( ) ( ) b = u u 5 u u 0 5 f( ) 0 0 y 0 y = y u = log y = = y u = log [8( y)yy ] = log ( y y ) 0 y 0 y = 0 y y y ( y = 0 = y = = ) 6 = y = u = log = y = 0 6 6

74 = cos y = 6 si y = 6 ( ) = y 6 0 y = cossi = si( ϕ) 0 0 ( y) = ( y) = k + k k = (k) k 0 f(k ) = (k ) (k)(k ) 0 f(k ) = (k ) (k)(k ) 0 0 M k = { 0 k N} k + k ( ) + 7 f() = lg R N f() ( ] ( ] ( ) 0 ( ] [( ) + ( ) + + ( ) ]

75 g() = [( ) + ( ) + + ( ) ] ( ] g() ( ] g() = ( ) ( ) 8 y = t = (t 0) y = ) 9 y = f() ( ) y = f( ) y = f( ) y = f(u) u = t = t t = y = f( ) [0 ) 0 f() = + () f() + f() = + = + f( ) f( ) = + + = ( + )( + ) ( )( ) 0 0

76 () f() ( N ) ( ) f() = g() = () f() g( b) ( ) b () y = f( ) y = ( + ) y = g() y = ( ) y = ( + ) ( ) y = (y 0) y = y = ( ) (y0) = 0 = = ( = () y = f() y = (0 0) r = (y 0) y = g( b) y = b f() g( b) ( ) ( ) ( ) y = b ( ) b b = 5 b = 5 ( ) () f() =

77

78 A cos B si C cos D t k k k k (k Z) b siasib (R R R b ) b A B A B b R R siasib

79 6 y = si( R) = ( y) ( ta 8 ABC = t B b 9si = t = 50 f() = si( ϕ) A ϕ = k (kz) B ϕ = k (k Z) C ϕ = k (kz) D = k + ϕ (kz) 5 y = si(tt )

80 A C B D - cot 5 y = + cot A B C D 5 y = si y = si y = t cot y = si T = (0 ) cos + si 5 y = cos si C D 55 y = sicos( t ( + ) ) 8 + t ( + ) 8 C D 56 y = si( + )

81 b A [k 7 k ](k Z) B [k 7 k ](k Z) C [k 7 k ](kz) 6 6 D [k k 7 ](kz) 6 6 B = cos ABC cosa 58 y = si( ) y = si( ) y = y y A C D 59 y = f() Ay = cos( ) B y = cos( ) C y = cos( ) D y = cos( ) = A y = si( + 6 ) B y = si( ) Cy = si( ) Dy = si( ) 6 6

82 6 si = m m m A ( 0) B ( ) C ( ) D ( ) m 0 m m 0 m m m m m + 0 m m A [k k ](k Z) y = siy = si B y = cos( ) si( si) Cy = si Dy = si si k 0 y = si A cos( ) = si B y = si( si) = si = C

83 6 y = si( ) y = si A y B y C y 6 D y 6 y = si y = si( ) = si y = si( ) = si( ) 6 si 65 cos = 5 si 7cos si+ cos 9 5 A B 5 9 si cos = 5 t = si = si + cos 5 cos = 5 si 7cos = ( ) 7 ( ) =

84 C D 6 y = (cos ) 68 si = si B = k k Z C { = k = k k Z} D { = k = k k Z} 5 69 y = si( ) A = B = C = D = = k = k y = cos = k = k At cot B t cot C si cos D si cos

85 k k k k (k Z) t cot A 0 OM 0 M P OM M P OM si cos C D 7 f() = si cos B f(0) = A B cos 0 si f() C 7 si = t 5 A B C D

86 t B C D A A [ ] B [ ] C [ ] D [ 0 ] A ( ) B ( ) 5 C ( ) D( ) ( ) A 75 f() =

87 = si ( = 5si( ϕ) ) ϕ cos ϕ = si ϕ = 5 5 ϕ ϕ [ rcsi rcsi 5 5 ] si( ϕ) ( ϕ ) si( ϕ) si( rcsi 5 ) = si[ rcsi 5 ] = cos(rcsi 5 ) = cos(rccos 5 ) = 5 si( ϕ) 5 f() 5 76 y = cos( ) y = cos( ) = cos( ) k k k k y = cos( ) [k k ](k Z) b = b =

88 b 0 = ( ) = ( ) = y = m + 78 y = si cos t cot si cos t cot = m (m ) 0 tatb = m0 tatb = m 0 m 5 ta + t B m A B t(a B) 0 = 0 tat B ( m+ ) m 5 si = si (si ) t = si 0 t = t ( t ) f(t) = t (0t ) ( t ) f(t) = ( t t ) f(t) [0 ]

89 8 f() = si cos + si f() = f() cos ( ) P u = cos( u ) u v = v = si ( v ) 8 y = k k + b ( b ) y = k k + 6 = k k + k = f() cos 8 y = si + cos + ( 5 ) y ( 5 )

90 [0 ] f() = si cos = si( / ) [ ] [ ] 85 f() = lgsi cos (0 ) cos 0 [ ] (0 ] f() k k (k Z) cos ) = cos cos f() 8 T = = si siy = siy cos y = si( ) [k k ] 8 8 (k Z) f() = + si cos + si + cos y = t si t cot si cos 7 T = siycos si siy = siy = si T = sicos = si si siy = si si = t

91 t = t [ ] T = t t (t [ T m = 9 ]) y = si( ) y = siu u = () α α α α = si cos + si f() = cos si + cos + si + cos f() = t f( ) = f() f() sicos 0 k k y = si( ϕ) y = t( ϕ) k k k k (k Z) k = m(m Z) m m ( ) si cos t cot

92 5 k = m (m Z) m m ( 5 ) si cos t cot 88 y = t( ) cos 89 y = cos(si) 90 y = + coslg(si ) cos 0 cos si 0 si k k (k Z) k k (k Z) { k k k Z} { k k k Z} t = m m + = 5 m m m 5 9 si cos = cos si 8

93 (cos si ) = si cos = cos si 0 cos si = 9 y = Asi( ϕ)(a ϕ ) ( ) ( ) 6 S = y = si( ϕ) X = ϕ + ( )S = ( ) + y = si( ) 6 95 ( ) si ( ) si ( ) si = y y y 0 y si 0 7 { k } { k k } 6 6 (kz) 96 t 9 t 8 7 t 9 = t( ) = t ( )

94 y = t ( ) t t 8 7 t 9 t 8 7 () f() = y + + ()y = (cos ) cos = y + + y mi = ( ) = cos = y + + y mi = cos = y y mi = ( ) f() = ( ) () ()f() = = = 8 = y = (cos ) 98 f() = sicosbcos f( ) = 6 f(0) 6 = 8

95 6 = f( ) = 6 b (cos 6 ) + cos f() = si8cos = si 8 = sicos = 5si( ϕ) t ϕ = cos( ) = si( ) t( ) = sec t sec + + t sec = + sec t sec t sec t t sec t = + sec t = sec t + sec t = sec t + sec t = sec t + sec t = sec t + sec t

96 sec = sec t = t = (si ) si si si = = k (k Z) y m = si = = k (k Z) y mi = si si = b = c = y = c b = si y = m si si y = 0 = 9 ( y) 0 y y = y = si = m (k Z) y m =

97 si 0 0 t cos k = t k = si OP PA cos si () 0 k OP k PA t cos () = si k = k = t OP PA cos () si k OP k PA t cos si 0 si cos = + cos + si cos+ si + cos + = k si cos+ si = k cos = k (k ) + k + k ( k + k ) (k ) = k = 0 k = + k 0 y = si + ( (0 )) si

98 u = si v = uv = (0 u ) si uv = (0 u ) u 0 ( ) y = 5 mi cos si 0 0 (si ) (cos ) 0 0 si cos + b 05 ABC c = ABC coa + cosb + b c = cosa + cosb 07 y = Asi( ϕ) k A ϕ k

99 A = = k = + = = 5 = 6 6 ( ) y = si( ϕ 6 ) = si( + ϕ) 6 si( + ϕ) = + ϕ = k ϕ = k (k Z) y = si( )

100 + si + si (si ) (si ) + si = + ( t) = ( t + ) (si ) t t = [( t ) + ]( t0 ) t t 0 t t = t t + si ( ] (si ) si + si + 09 y = cos si s = cos si A s t = s = cos si = si t = si si 5 si = (si ) 5 s 5 M( ) N( ) + k BN = k BM = y 7 y y m mi 7

101 y y R y R R R R si y ( ) + cos ) y b y y y [ ] b c S / p ( p ) + ( p b) + ( p c) = ( p )( p b)( p c) p S ( b c) / S ( b c) / S b c S b c S / b c b c S / + b + c cosa cosb cosc = + + bc b c

102 b + c + c b + b c + b + c + + = bc b c c b bc ()f() sisisi () t t f() () si sisi si cos T (k N) k cost sit 0 ( Z) k k k T si( ) cos( ) si cos y si cos

103 A B 0 C D t sec t t 8 f() M N cos A B C D 0 y si siy A B C D 5 A B 7 C D

104 ( ) cos si 0 A B C D f() si + cos A k k k Z B { k k k Z} 6 C { k k k Z} D { k k k Z} y lg si cos si + cos A { k k k Z} B { k k 5 k Z} C { k k k Z} D { k k k Z} 6 y cossi ( )

105 A [0 8] B [ 5] C [ 5] D [ ] A B C D 8 si si (coscos ) (0 ) A B C D 9 t t 0 ( ) A B C D cos y si cossi si( ) 5 cot cos( ) A B C D

106 si t + t 5 + t cos( ) cos( ) 5 5 sia 0 sib 0 siasib si B si A = sibsia cosa cosb cos cos f() cos cos cos cos f() = cos = si f() cos f() si sicos b( 0) [0 ] [ 5 ] b f() (cos) si b si( ) 6 [0 ] 7 [ ] si( ) [ ]

107 ( ) b 5 ( b) A B 0 C k k (kz) D k k (kz) y si( ) 0 si( ) k k k k (k Z) 6 (0 ) At si Bt si Ct cot Dt cot

108 8 t( ) t t( ) 5 A B C D 8 t( t( ) t[( ) ] ) t = + t( ) t 5 9 cos m si + m m + m m A B C D 5 5 si 0 (C) (D) 5 m 0 cos m cos + m si = (A) b A B b ( R ABC ) R R (t t ) 6 A () B () C () D ( )

109 t t t ( t t ) 6 6 (t t ) ( t t ) t t t t t t t t 0 t ( ) + si8 + + cos8 (si + cos ) + cos y si( )si( 5 )cos ( ) A B C D cos cos si si = ( cos) 8 0 y ( si)(cos) A 8 B ( ) C D si 0 si 0 [ ( si ) + si + si 8 ] ( ) = 7

110 b c ( + b + c ) ( 0 b 0 c 0) 5 (0 ) y ( cos) si 6 A B C D y ( cos) si (cos ) si 0 cos 0 si 0 y cos cos si cos cos si [ ] 7 y 9 6 y sicos y 8 A B C D f( ) f( ) 8 8 si( ) cos( ) si( ) cos( ) si( ) si( + ) cos( + ) cos( ) cos( ) si( ) (D) si( )si

111 A 5 B 6 6 C 7 D 8 8 (D) 0 y 5 6 ta tb tc tatbtc( A B C tatbtc tatbtc 0 tatbtc ta tbtc A B C 60 ta tbtc 9 t t si cos + cos 50 ABC b c t A t C 5 ABC cos(b C) A) [ ) si0+ si0 5 cos0+ cos0 si80 si0 5 si70 5 (si cos ) (0 ) t

112 56 y cos( ) cos( ) 57 5cos( ) 7cos 0 t t ( 5 ) {0} 9 59 t( ) t( ) si( + ) si( ) t( ) t( ) + cos( + ) cos( ) si = cos cos( )cos( ) cos cos si = 60 t( ) si cos + t t t + cos si cos si si cos si t t cos + t + t si cos 5

113 5 f() cos si + si( + ) 6 y cos + cos( + ) si + si + cos si + cos y = cos + cos si cos si si( + ) 6 t( ) 6 cos( + ) 6 cos0si0 cos70cos0+ si0 cos0 (si0cos0 cos0si 0) si0+ si( 60 0) = = cos0 cos0 si 0+ cos0 si0 = cos0 = si0+ cos0 = cos0 si( 0+ 0) = cos0 6 si si cos cos

114 cos( ) si si 0 si( ) 9 65 si csc cos( ) si cos si cos t = + si si + cos t = = + t cot + t si si si si = B C 80 ( ) 90 sicos ( ) si d cos d si cos ( d) ( d) 5 9

115 d d si cos 0 d si 0 cos 68 0 si ( cos ) y si ( cos ) y si cos y si cos cos 6 ( ) 7 y y m si 0 cos 80 si0 cos80 si0 si0 50 si 0 cos 80 si0cos80 /

116 0 [ ] + y0 t t COP 0 7 k = = y = 5 z = 0 u = 0y 0 0 = 0 + y f() + [ ] f() f() f() si( ) [ ] 0 [ ] f() f() si( ) si( ) [ ] 0 si( ) [ ] si( ) [ ]

117 si( ) [ ] sicos 7 y si + cos + si cos 0 y ( 0) A si + cos ( ) usicos ( u u ) u (v / ) vsicos ( v / ) / 0 k AP = ( ) + / 0 k AP ( ) + = + y ( ( ) / ( ) / ) 0 cos + cos y si + si 0 = =

118 y ( ) 0 [ ] cos cos [ ] si( cot cot + ) cot8 cot7 cot6 si si si90 si90 ( + ) cot5 si8 si7 si 6si5 ( ) + ( ) cot5 si8cos8 si6cos6 ( + ) cot5 si 6 si 7 (si7+ si 6) si5cos8 cot5 si6 si7 si 6 cos8 cot5

119 c si y t B( ) t m 5 si cos [ ] 76 si coscos si si cos cos si t [si( ) si( )] [si( ) si( )] t y t A(0 ) t mi y t B( 0) t m cos si [ ]

120 u y u u si cos u u sicos y u u si( ) u u y u = (u ) u u + [ + ] 78 y + (0 ) si cos y + = si cos sicos si si cos si y y 79 f( ) = si cos si k y cos

121 k 0 0 k + 0 (0 0) k + k 0 k f( ) [0 ] t( ) 80 = si t( + ) t( + ) = t( ) t( ) t( + + ) = + t( + ) t( ) si( + )cos( ) + cos( + )si( ) si( + )cos( ) cos( + )si( ) si si si 6 si 8 y cos + y + y si( ϕ) y(t ϕ ) + y + y si( ϕ) + y + y y ( ) b ( )( b ) b ( )( b ) si si ( si )( si )

122 si si cos cos 8 = = cos( ) si( ) si( + ) cos( ) + si si cos si = = si( ) si cos + cos cos + cos cos si si = = si( + ) + + si cos + cos si cos si t = t ( ) cos( ) = = 5 + t + ( ) 9 cos( ) cos cos = 0 si = 0 cos + cos cos + si cos si( ) ( si ) = = 5 cos + = cos( ) cos + = 0 5 si + bcos 8 b 5 5 t 8 b 5 cos bsi 5 5 b t + cos 5 = 5 b t 5

123 8 8 b t t t t( ) 5 = = = t t t + cos+ cos+ cos cos cos cos + cos cos cos (cos+ cos ) = cos cos (cos+ cos ) cos ( t ) t cos 6 = 5 + t cos( ) 86 y cos ( ) cot t + cos + cos( ) y cos si si cos si (si ) si( )cos( ) si( ) 87 f() cossi cos ( R ) f() (si ) 6 0 si f() ( ) 6 0 si f() ( ) 6 88 cos( ) si( ) ( ) 9 (0 ) cos( )

124 0 cos( ) 9 5 si( ) 9 5 si( ) cos( ) cos cos ( ) ( ) 7 cos( ) cos ( 89 t t t t + ) si si si coscos si = cos si si( ) cos cos cos si si = cos cos si [si( ) si( )] ( si si( ) si ) si cosa + cosb 90 ABC cscc ABC sia + sib A + B A B si cos A + B si(a B) = t A + B A B cos cos si A + B A B A B + + cos = si A B + A + B A + B 0 si 0 cos 0 cos A + B = A + B = A B ABC

125 si B+C B+C B+C B C cos B+C B+C cos cos cos = si cos B C B C A ABcmACcm Rt ABC S AB AC6(cm ) b + c + c b = b ( b )( c b ) 0 bc c B A C 9 ABC b c cos = cos cos () t A C t = () t A+C () cos B cos A C cos si A + C cos A C cos (si A C A C A C cos + cos si ) = cos cos A C A C cos cos t + t = A C A + C t + t t = = = A C t t

126 (0 ) bc 6 B C A b c b c 0 95 ABC si A cos A b + c si A cos A cosa A A R[si B + C cos B C sia] A b c R(cos B C ) B C cos B C b c B C cos B C b c 0 A b c R(cos B C ) 0 ( + z)( y + z) + ( z)( y z) y z z 0 0 y coscos (0 z z ) y

127 ( + z)( y + z) ( z)( y z) + y y z z z z = ( + )( + ) + ( )( ) y y = ( + cos)( + cos ) + ( cos)( cos ) = (cos cos + si si ) = cos( ) A 8 A si si si R (si) R si z mi 99 y +

128 y ycos t si ± sec ( y) + si( + ψ) = ψ ψ ± si( ψ) ( y) + ± y ( y) + 8 y y mi A B C ( ) ( ) 0 0 ABC cota cotbcotc ABC + 5cosC cos(c B A) 5 + cosc

129 t + t A A ( cot C) = ( + cot C) = 9 t C 9 + t C + 5cosC 5 + cosc = + t + t ( 5 ) ( 5 C C ) + t C + t C 9 t C 9 + t C + 5cosC cos(c B A) 5 + cosc 0 ABC bcosc siasi( B C) sic(si B + si A) sibsi B sib(si B sib) cosbsi B si B sib cosbsi B si B si 5B si 5B sib si B cos 9B 0 0 B si B 0 cos 9B 9B 0 B 9 ABC A B C ta tbtc ta tb tc tatbtc

130 ta tb tc ta tb tc / (ta tb tc) ta tb tc A B C t t t 9 A B B C C A t t + t t + t t A B C t 0 t 0 t 0 A B B C C A t t + t t + t t A B C t t t A B C t t t A B C t t t 9 + y y 06= y + y + t y t ( + y ) y t( ) y + y + t t coscossi si = + + = t t coscos sec sec = cos( ) = = + t ( ) + b c + d c bd 07 m m m (bc 0) b c d d + bc

131 b d + + c m m = b d c b d = t = t c + t m t( ) t t 0 t log log t t = = cot( + ) t t = t( ) ( ) ( ) ( ) t( ) t( ) t( ) t( ) t( ) t( ) ta + t B + t C ta t Bt C = + + t A t B t BtC t C ta t A + t B + tc = t A t BtC cosa cosb cosc + + si BsiC sicsi A sia si B cos( B + C) cos( C A) cos( A B) si Bsi C sicsia sia si B

132 5 sia sib sic 5 csia sic 0 = 0 = b cos A si A cos B si B + + cos B si B cos A si A ( ) + b b cos B si B ( b) b + = + cos A si A t t + t + L+ t = cot cot t = cot cot t = cot cot L L t = cot cot

133 S t sec + t sec + L+ t sec + t ( t ) tsec t = t t t = t ( ) t k t k sec k = t k t k S t t 5 S + + L+ + t t + t t + t t + tktk = = t k + t k + t k t k t k = cok = = + si si cos k [si( k ) si( k ) ] si si( + ) si S si t B cot C y AB AC B C si B + cosc t cot = + cosb sic

134 si B + cosc = sic + cosb + 5 AC AC AC + 5 = + + = AB AB AB = 6 = = cos( ) 0 si( ) si si (cos ) b R = b R sib bsia

135 0 ABC cosacosbcosc 8 bcoscccosb bccosbcosc bccosacosc ccosacosc c cosb bcosa bcosbcosa cosacosbcosc 8 C A cos ccos b c b c b b t( ) e t (e e ) t( ) t + cos( + ) + + si cos si( + ) e t = e ( e ) e

136 k k t t t t k k t( ) k 9 k 0 0 k k 0 t( ) t( ) cos ( ) y = t( ) si ( ) cos ( ) si ( ) y 0 y [ 0] (0 ) ( ) t( ) t si( ) si = cos( ) cos

137 0 6 t = cos + si + cos + si si + si cos cos + si cos si (si + cos ) = cos (si + cos ) = t = t t t (t ) sec sec cos cos cosa + cosa 8 t A + cosa + cosa cosa + cos A + cosa + cos A ( cos A) cosa = = ( ) ( + cos A) + cosa ( y) + y( ) = ( ) + y( y) =

138 si y si 0 0 sicos cos sicos cos si cos si (si ) si( si( ) si( )cos( ) cos( ) = 0 = = = 6 = 0 = 6 = = ( y) ( 0) (0 ) ( ) ( ) 0 0 t cot ( ) L cot cot = (cot cot ) + (cot cot ) + L + (cot cot ) + t 0 cot cot (*) t t ( ) L (*)

139 cot cot ( ) ABC si A si B si C 9 A B C ( cosa) ( cosb) ( cos C) (cosacosb) cos C [cosccos(a B)] cos (A B) + 9 = cos (A B) = cosc = cos( A B) A = B = C = t t t( ) = t t si ( ) si( )cos( ) cos ( ) [t ( t ( ) ) t( ) ] + t( cos ) + cos = t cos t + t + cos si cos k k

140 si + b b ( ) t b b = + b b ( ) cos b = b + b + ( ) ( b ) b cosbsi + + b + b cos 5 si (cos si ) = + si + cos + si + cos cos si cos si = + = + si cos + si + cos si cos si cos = + = + cos si + cos+ si cos si (cos si ) = + si cos si cos cos + si 5 6 y cos si 5 t t t + t + y 7t 6t y t 0 7 [(y ) (7y )(y )] 6(y )( y) 0 y t y 7 y y

141 si si si si 7 S L+ m m sm s sik k k (k N) k k m L+ m m + [ ( ) ] m = = [ ( ) ] [cos( )] [ cos( )] [si( ) [( y) (y z) (z ) ] 0 0 ABC b c si A B C si si 8 A A b + c si cosa si bc ( b c) = bc bc A si bc

142 sib B b C c si c b A B C b c si si si = bc c b 8 () f( ) f() f() f( ) y f() f(y) f(y) f() f( ) f() f( ) 0 f( ) f() () 0 () f( ) f( ) f( ) f( ) f( ) f( ) f( ) f( ) ( ) 9

143 9 9 ( ) 9 9 ( ) log log log ( ) log log ( ) ( ) log log ( ) [ + L+ ( ) ] log = log ( ) ( ) log log ( ) ( ) { } ( ) 0 log ( ) log + + { } + + { } + + { }

144 0 0 0 f( ) f( ) t t f( ) f( ) f(t ) f(t ) t t f( ) f( ) t t t t t t f( ) f( ) f(t ) f(t ) f( ) f( ) f( ) f( ) 5 b c R blg b c lg

145 ( b lg) (b c lg) (c lg5) = ( 5 (b ) (c ) lg 0 b lg b 6 c lg c lg5 6 R(i ) 0 i= i i i i i= i i= 0 i i i= i ( + ) i i i= i= i ( ) i i= i i= i f ( i) = ( + ) i i = f( i) f( ) = i = f( i) f( ) = f( i) = i = i= i i ( ) i = i= i i= 7 y = y = 0 y 7 i= i )

146 ( + b) 8 5 y = + y = ( b) A ( b) ( ) u = ( u0 ) v = b = ( ) b = ( ) ( ) ( ) b = + 6 b = = b f() f() f() f() f() f()

147 f() f() f() = f() f() f() f() f() f() y y tcos y tsi t 0 0 y y = t (si ) u y y ( + ) = y y [ ( )] = y y u t (cos cos si si ) t (si ) =

148 ( ) = C C C C = = ( ) 5 b c b bc c = b c [(b) (b c) (c ) ] (b bc c) b c b = c ( c ) ( b c ) b π = cos = si 0 c c ( c ) ( b ) (cos ) (si ) cos si = c L+ ( N) = + + L L+ ( ) = + ( ) + ( ) + L+ ( ) ( ) = N

149 y = ( ) 0 y y = R 0 (y ) 6(y ) 0 y y = by + cz by cz ( ) 8S yz ( = by = cz ) 7bc y + t + t y = = + + = t + [ ) + t 5 y = + = m m 6 b 0 c d 0 m 0 c b d

150 c b d m 0 m c m b d S S S S z ( )si60 ADE FEB CDF ABC ( y)si60 y( z)si60 si60 65 f() = ( 0) g() = g() 0 g() = ( ) f() = = = g() ( 0) ( + + ( + ) )( ) 0 ( 0 + ) 0( 0) ( ) 999!

151 = L + L L ( + ) +! ( )! 999 y + y + y yz + z z z + AB + y y cos60 = y = y BC = y yz + z CA = z z + y + y + y yz + z z z +

152 70 ()rcsi 5 rcsi( ) 5 A rcsi 7 B rcsi Crcsi D π 5 rcsi 5 = rccos = rccos rcsi π π π () 0 rcsi[cos( )] rccos[si( )] bi = ( bi)(cos + si ) ( ) ( i) π π 0 = A cosθ k = cotθ 0 siθ

153 π A B ( 0) R f( rccos ) f[ rccos( ) ] A { } B { } C { } D { } rccos π rccos( ) π rccos 0 0 rccos( ) π 7 rct( ) rct( ) rccos π π π π A B π π π π C D π rct( ) rct( ) t[rct( + )] + t[rct( )] (+ ) + ( ) = (+ )( ) = t[rct( + ) t[rct( )] = rccos = rccos( ± ) = π π θ cos = + siθ siθ

154 π A B rct( ) C rct( ) rct D rct t = b θ θ θ θ θ cos = (si + cos ) (si cos ) θ θ θ θ = si + cos si cos θ θ θ θ θ si cos cos = cos cos = 0 θ θ θ θ θ θ si cos cos = si t = = rct = rct rct = rct ( ) π π 77 (si )cos = 0 rct 5 5 π π A B 0 0 π π C D 5 5 rct rct t( ) = tα + tβ + = tα tβ

155 π π = si cos 5 5 π si 5 π t( ) = = cot π 0 cos 5 π π l cos 0 = si π π 0 0 π 0 (0 ) 0 π 0 78 rct rct + π π A B π 5π C D π 5π si + cos 79 rcsi = π π A B π π C D

156 5 5 A k B k 5 5 C k 0 D 0 k C 5 D rct rccos( = ) = rccos + rcsi 86 f () f () = cos( ) f () = rcsi f () π

157 87 f() rccot rct D (0 π ] π A { } B { π } π π C 0 D π 89 y = rccos A si(rccos ) si(rccos ) B t(rccos ) t(rccos ) C si[rccos( )] si[(rccos( )]) D t[rccos( )] t[(rccos( )] rccos π π rccos( ) rccos( ) π π (0 ) ( ) t[rccos( )] t[(rccos( )] D

158 A [0 ] B C 0 D π π A B 6 π π C D π rctb = B π π 9 f() si cos B π π π π f() si( ) 6 π 5π π 57 si( ) 6 D

159 π D [rcsi rcsi] π π 95 y = si [ ] π π [ ] y = rcsi [ ]

160 96 rcsi b = rccos c = rct b c cos[rcsi( ) rccos( )] A B C D 5 5

161 rcsi( ) MP OM 5 rccos( ) MP OM 6 MP = M 5 P = OM OM = Rt OMPRtOMP P O P 5 5 rcsi( ) rccos( ) cos[rcsi( ) rccos( )] 5 π π A B π π C D π = rcsi[si( )] rccos[cos( )] π π π π π (0 ) ( 0) ( ) π = ( ) π = A π π = y m = ( ) =

162 π yrcsi(rccos) 0rccos π cos cos 0 [0 ] rcsi( ) rccos rcsi( ) rcsi( ) rcsi( 0) rccos( ) rccosrccos( 0) π y 6 π y 6 0 I = { t(rct) = } A = { rcsi(si) = } B = { cos (rccos) = } C = { rccos(cos) = } B I C A B π π I = R A { [ ]} BC = { [ 0]} A B = A B { ( ) ( )} = si(rcsi) π y = y = cos(rcsi)

163 π rcsi cos(rcsi) 0 y 0 si(rcsi) y = 5 k = cos cos (cos ) cos 5 5 (cos ) [ ] 5 k [ ] π 05 [0 ] cos kcos k π cos kcos k [0 ] cos k cos cos f() = [ cos + + cos cos ] cos = cos k cos k ( ) π 06 [0 ] cos msim 0 m π 0 0 AB g() m CD(

164 m( ) g() AB m m π si ( ) = m π π 5π 0 π 5π π 6 [ ] π π π π π m si( ) m 08 f() = rccosrccot π π π π rccos [0 ] rccot [ ] f() [ ] 8 8 z = ( ) + ( + )i z = ( + ) + ( )i z + z ( ) = ( + i) = ( i) = = = i i

165 u = si v = u v = (0 u v ) si v f() = 5 [ 5 mi ) y) = cot cot y cote = cot(a B) = cotf cot(c cot + cot y 8 = cot(e F) = = + 8 π π t( + rccos ) t( rccos b ) b 0 b rccos b = 0 b 0 π α α π π α + t t t( + ) + t( ) = + α α t + t

166 = + α α ( t ) + ( t ) = α ( t )( + t ) α α + t b = = = α cosα t [ 7 ] k = = y = z = u = rct rct = t = t + π π π rctrct( ) π π π t( ) = t α + β + t = + = + = tα tβ + + π π π ( ) = π π cos si m = 0 t = ( t ) t [ ] y = m

167 5 si sicos cos = 0 t t 0 t = t = π t = = k (k Z) π t = = k (k Z) 6 π π { = k k k Z} 6 k k si si k k = (si ) (si + ) 6 k k 6

168 7 A = {( y) m cos y = si } B = {( y) = t y = 6t t } A B m ( m) y A (m 0) + = B y = 6 9 = 6( ) ( 66) m A B ( 0) A (m 0) A (m 0) m 7 m m M A B A B M π f() si( ) A B π A B 0 f() f() = si( ) π 5π 9π f() M m[f() 0 ] π f( ) f( π) f ( π) 8 8

169 π + A + B 8 5π + A + B 8 9π + + A B 8 π A + B0 8 5π A + B0 8 9π + A B 0 8 B 0 m[f() 0 ] π = m{ si( ) B 0 } = B mf()}0 m[f() 0 ] = π π 9 = si + cos ( N) si π cos π si( π π + = + ) 6 T = π = ω y = f() = si( π π + ) 6 π π = si + cos = = 0 cos = sicos kπ π k = π π 8 kπ k k = m k = m k = m

170 π π = mπ mπ m 8 8 b y = cos + b si + si + bcos y b (b) si b si = y = ( b) y = ( + b) si = 0 y = b by = + b Z

171 b + b A b ( ) B b ( ) C b D b ( ) )(b b ( ) ( b ) ( )(b ) b = ( ) b = = b b ( ) y = +

172 y y y = y 0 + y 0 y(y ) 0 0 y 5 () f() ( ) g() ( ) ( 0) f() f() = 0 f() g() = ( ) ( ) = f() () b 0 ( b) b b b = + ( b) b b b ( ) b b = ( + ) + b b ( ) b b ( ) = b b ( ) = b b = = b b b ( ) 6 M { } N = { log ( ) 0} M I N

173 A { 0 } B { } C { } D { 0 } M { 0 } log ( ) 0 0 N = { } log ( ) 7 0 b b log b ( ) B { 06 } ()( ) () 6 ( )() 6 ( )()

174 6 0 [ 6) U ( 0 ) = ( 0 6) () b 0 { } + b 0 b 0 = = b = b b = = 6 6 = b = b = = 6

175 A( ) () b R + b b = + b ( b)( ) b ( b)( + ) b b b b = + b () y z N y + y z z ( z)( + ) y y z ( b)( + ) ( z)( ) b y y z

176 ( b )( b c b c bc) ( b c)[( b) (b c) ( c) ] b c ( b) (b c) ( c) 0 b c bc 0 b c C [ ) D ( ) 5 ( ) D 6 0 A 0 C D ( ) B 7 y = 5 k + 50 k k + 50 (k5) 5 0 y 0 + 5

177 8 log A ( ) B ( ) C (0 ) ( ) D (0 ) ( ) y = log log log log 0 y = log log log log 0 (0 ) ( ) C A A B = R B A B = R C A B = R D A B = R 0 I = R M = { lg 0} N = { } AM N BM N C M N = D M N R A { } B = { } A B

178 + A lg B lg Clg D lg B b D b 7 R M { lg 0} M

179 C + D + 9 b 0 ( ) b A 0 B 0 C D + C 0 + D + A b b B ( b)( + ) b + b C b b b D b + b

180 5 ( 0) A { } B { 0 } 5 C { 0 } 5 A 0 cos( ) cos() B 0 y 7 C y y = log ( ) 8 5 B (0 ) C ( 5 ) 5 D ( )

181 59 M = ( ) N = log ( ) R M 6 60 { + 0} { log ( ) 0}

182 A b B b C D b 66 y = log ( k k) k 68 log ( ) log ( 0) lg 70 0.

183 7 = + + L+ p = ( ) ( ) ( ) q = () ( ) ( ) lg p = f(0 ) q = f(t π π ) r = f(si cos ) [0 ] 7 R f() [0 ) f( ) = 0 f(log ) 0 8 A (0 ) B ( ) C ( ) ( ) D (0 ) ( ) A lg Blg C lg D lg

184 77 + A ( ) B [ ] C [ ) D ( ) 0 0 y y y 0 y y 0 y A { 0} 5 B { 0} C { 6 0} D { 0} 8 y = log ( 5) [ ) A 6 B 60 6 C 8 6 D 8 6

185 A B + y y C y D y 87 f() = + f () 88 ( 0) + 90 A = { 8 = 0} B = { + } 9 b c R + b c = b c

186 ( ) ( ) ] ( ± 5 ± 5 ) 67 = 0 = y ( )y 0 R y y ( )y y 0 y y + ( ) (*) y + R ( ) + y + (*) R y y 0 y y

187 = ( ) 0 g( ) = 7 0 g() = ( )( ) 0 k + k R k = ( ) 0 = k 0 = (k) 8(k ) 0 k y = + π π = si [ 0) ( 0 ] si cos ( si ) y = = = ( + t ) + cos si + cos π π [ 0) (0 ] t t 0 t = y m = = t = y mi = 0 =

188 f(0) = m 0 f() = m m 0 m 0 50 y = = y si = y cos y = (cos + ) cos = 0 y = mi [ ) (0 ) y 0 π 50 + π π = t ( ) t sec π π si 6 t { } 505 y k + y 0 y 0 y k y 0 y 0

189 + y k 0 y 0 + y + y w = w = + y + y y y = + y + y + y y w w 0 = y w = m w (0 ] + y k k w m k k + y [ ) 506 y R + y = y k 0 k ( ) = k( y) ( ) = (k y y ) (ky ) k( ) y k = = k ky = y = y y = k k = y = y = ( ) = y 507 f() = lg L + ( ) + [( ) ( ) ( ) ] ( * ) f() = [( )] ( ) ( ) ] (

190 ( ) ( ) ( ) ( ) ( ) ( ) f() = [( ) ( ) ( ) ] f = mf() = f() = [ ] = m ( * ) f = m ( ) 508 log ( ) f() = f( ) = f( ) f() = = f = mif() = f() = = mi 7 log ( ) + 5 ( + 5 ) yy = r r cos si = r (si ) r = si = = y =

191 y y [ 7] 50 b c b c = y = +b + c + y = ( b c) ( +)(b + ) (b +)(c + ) ( + )(c +) ( b c) ( b ) (b c ) ( c ) = ( b c) 9 = y = b = c = / y = b = (b ) = ( ) [( + b / + b / b b ) ] = ( + b ) 6 = 0 = b = ( b ) = 0 b = b = y = ( 0) y = = = 8 = = y = 5 0 y = () 0 0 y = () = ( ) = + + ( ) ( ) = 9 9 = = 9 y = ( A A )

192 = t = t (t 0) 5 5 y = t t = (t ) 5 f() = 55 log ( ) + + f() = + + f( ) = f( ) f() = = 0 + ( + ) f() f() = = 7 f() log ( ) 7 log ( ) log ( ) + 5 = + 5 m 56 f() = + π π = t ( ) + si y = sect = cos π + cos( ) = π = cot( ) π si( ) π π (0 ) y (0 ) 57f() = f() = ( ) + ( ) ( 0) + ( )

193 ( + ) ( + ) ( )( 0( R ) A B A B A B A B ( + ) ( ) ( ) ( + ) ( ) f() = ( )( A B A B f( ) 0 ()( ) 0 f() 0 0 y y = 5 59 y z y z R + = 9 z y = 6

194 ( y y ) cos50 = 5 ( y ) z = z ycos0 = OA = OB = y OC = y S = S S S ABC AOC AOB BOC = y y zsi0 si50 z 6 = z y yz yyzz = f() 0 0 ( ) 9 0 f() f() = + 5 g() = ( ) 5

195 = + ( 0) 0 ( + ) = k y = k 7 z = k u u = (k 6k 9) = (k) y z k k k 0 7 k [ 7 ] k = = y = z = u = 7 k = = y = 5 z = 0 u = N = 0 b c d = = b = c = d = M = 6

196 55 z = + y y + + y + + y y + y + z = + y y + + y + + y y + y + z = ( 0) + ( y ) + ( + ) + ( y + ) + ( ) + ( y + ) z ( y) A(0 ) B( ) C( ) 7 AB = BC = CA = ABC 0 + ( ) + ( ) ( ) + ( ) = 56 f() = f() = = ( ) + ( ) + ( ) f()

197 y = y y = 0 = 0 0 C f() AB = 0 57 y = y = = ( ) + ( 5) = ( ) + ( 0 + ) ( 5) + ( 0 + ) ( ) + ( 0 + ) A( ) ( 5) + ( 0 + ) B(5 ) y = = ( ) + ( 0+ ) + ( 5) + ( 0+ ) y = A B A B y = A B = ( 5) + ( + ) mi

198 P ( 0) = 5 = = y 5 58 y =69 f( y) = y +0 +8y 0+ 8 f( y) = y y f(y) = + y + y y + y = ( + 5) + ( y + ) = ( 5) + ( y + ) (0 ) f( y) m = f(0) = y 5yy = 5 S = y S mi + y y + y + y y 5( + y ) 5 5y ( y ) S m

199 5 5 y ( y ) 5 y ( y ) S S S S = 0 S = 0 m mi = = = 8 S S 0 5 m mi 50 y z t 0 log 99log y99+ log z 99klog 99 k t log 99 + log y 99 + log z 99 k y log z t 99 t 9 g( y z t) = 9 y z (lg99 + lg99 + lg 99 ) lg 99 y z t 5 b b = b b b = b b y z t t = + + b b + b = + + b ( + )( + b ) + + b + b ( ) mi = = b = + + b ( y + y z + z ) + y + z { ( ) y + y z + z } m = + y + z 5 y =

200 y = ( + ) + ( ) y z R + y z = y z 0 ( y z ) = 0 = 9 ( y z ) y z 9 y z = ( ) ( y) ( 9 z) y z 6 = 9 = = y = z = y = z = y z y z = = 6 = y z 55 y = y + ( ) + y = + P( ) y = 0 P

201 y P 0( ) [ ] y 0 + [ ] P0R = AH = = [ ] 56 f(t) = t + t y = t = t 57 f() = u = v = u v = (u 0 v u v ) ( 79) f() = u v v = u f() v f() = OA = f() = OB = mi m 6 u v f() [ + ] ( 6 ]

202 59 y R y y = u = y p = si( θ + π ) 6 u = y = p [ ) 50 m [ 0) (0 ] f(m) = m m + f( m) = m m m = f(m) = m () m 0 = ( m + ) + m f( m) m m = = m m m + e 5 y = + e y = + + ( e ) + ( + e ) + ( + e ) y = P P + ( + e ) y = m PP y ( ]

203 5 f(t) = t t 6t + 8 = t y = t 6t y = (5)(0 ) y = (5 ) = (5) = 8 9 (5 ) ( 5 ) [ ] = 5 = = y m = y = + ( R ) + R + 0 y = + = + + = + + +

204 + = + = 0 y = mi 57 f() = f() = ( ) + ( + ) y = ( 0) y = = = 8 = = 8 y = 8 mi 59 f() = + c bd + b c + d f() = ( + / ) ( / ) + ( + / ) + ( / ) = 0 / 6 [ / / ] f( / ) = / f( / ) = / [ / 0 / 6 f() = (6 ) + + ( 6 ) [ ] = 55 f() = + + y = 9 y = = ()

205 y = 0 0 ( y ) = = y = 0 m y ( ) = = cos y = si 5 y = cos cos 9 = (cos ) cos = ( y ) m = 55 y = ()(0 ) 0 y 0 = 0 = y = 0 0 y = ( ) = 9 [ ( )] + + ( ) [ ] = 9 = [0 ] ( ) y = () y = ( ) = ( ) [ ] = + + ( ) 7 y = ( ) = = 7 V = 6 yz yz = 6V + y + z yz = 6V L = y z + y y + z z +

206 6V 6V 8 y yz z y z = ( ) 6V V = 5 7 ( L) L y = 7 ( ) ( )( ) ( 0) 7 = = y = 7 ( ) 557 y = + ( c ) b ( b c 0)

207 D P = + BP = (c ) + b y = D P BP = + ( c ) + b 8 D P B = c y = + ( c ) + b y = ( + b) + b mi + c 558 b c R + b c = + b + c + + = = ( ) ( ) b + (b ) c + (c ) + b + + c + [( ) (b ) (c )] = lg ( lg ) lg lg lg lg lg ( lg )( lg ) ( lg ) ( ) lg Llg

208 560 ( ) + + = = = = { } = f() = 0 f( ) f( ) + f( ) = f( ) = f( ) f( )

209 + + ( + ) ( + ) ( + )( + ) ( ) + 0 ( + )( + ) ( )( ) 0 ( + )( + ) 0 0 ( )( ) 0 f() = (0 ) + S 7 + N = T + 7 b S = ( + ) 0( + ) +0( + ) + ( + ) = = 0( ) = 0( )

210 b T = b = = S T = 7 + = 8 = b + 7 = = S b T ( + ) S = T = ( + ) 0 ( 0) f() = { ( )} f( ) ( N)

211 f() = f(0) k= k = ( ) f() = { ( )} ( ) ( ) = ( f() = ( ) ) {f( ) f()} = ( ) ( ) = ()S() = S(0) k = ( )( k= (5)S() = ( )( 00

212 S(7) = = S(8) = = f() = lg + + () f[( )] () () f(0) = lg = f ( ) = 0 f () = 0 = f () = 0 0 f ( 0) = 0 f(0) = 0 = = f () = 0 () f[( )] f(0) 0 ( ) ( 7 0) ( + 7 )

213 ( + ) ( ) ( ) ( ) 0( R) A B A B ( + ) ( ) = = ( )( 0 A B = f() m b [ m m] f() mb f() mb f() mb f() mb f( m) bm f(m) mb m mi mb m bm c bmm bm c mb m c 0 m c 0 () f() M M () () M = f() M () M = f(0) = b b b b b b b b =

214 b = b 0 b 0 = 0 f() = ( 0 0) y 0 () y = () y = y p( ) ( ) 0 0 y pz = p( ) ( ) 0 0 z = (0)(0 y) 00 y = z = 5( ) 5( ) { [ ] 00 } 00 5( ) 0 0 z 5( ) = () z = (0)(0) = + + ( +) + = + ( + ) ( + ) + + ( + ) ( + ) 0 = + + ( + ) ( +) = [( + )] + + ( + + ) = ( + ) + + { } = +

215 [ ] f() f() y = b 6b = = = cos b = si ( i ) ± = i D = k k ( k + ) ( k + ) (y 5)(y ) y (y ) 0 (*) 9 y (y ) ( * ) y = = y z m = m t y = m t z = m t t t t = 0 y z = ( m t ) ( m t ) ( m m t ) = + t + t m + t = y = z = m

216 5 ( )(b ) b b b = = t b = R + t( t ) 5 5 ( +)(b +) + t + t 6 6 ( )(b ) = = = 5 b b t t = 0 = b = = y = () 0 y = ( ) = 5 0 = y = ( ) ( ) 5

217 y = ( ) ( ) y 0 = ) = y ( 577 f() = + f() + f() ( N ) = ( ) = C C C C C 0 C = C C (C C C C ) = (C C C C ) 0 C = C C C C 0 N f() log log ( 0 ) log = t( 0) log = t t (t ) t t 0 (t )(t ) 0 t 0 t log log ( ) 0 (0 ) b R + b = b b f() = = b b 0 b f(b) = b 0 b b f (b) = f( ) = 7 7 mi b b

218 580 ( 0) 0 0 f() = ( 0) f() = ( 0) f( ) = + = = [ ( )] = = = f() ( 0) ( + ) + ( ) 5( ) ( 5) + + f() = 5 f( + ) f() f( ) = ( ) 5( ) = ( 5) = f() f( ) f( ) + +

219 ( )( ) b = b = b b + b 58 b N + b b + b ( )( ) + b b ( ) + ( ) b = + b ( )( b) = ( + b) b N ( b) 0 ( )( b) 0 ( + b) b + b ( )( ) 0 + b ( )( + + ) + 0 ( + + ) + + ( ) ( + ) 0 ( + + )

220 586 q 0 p q p q p (q )(p ) 0 ( q )( p ) 0 q 0 p { } p q + b + b 0 b b ( ) log ( ) log ( ) [ log log ( ) + ( + ) ] log ( + ) log log [ ] ( ) ( = = ) = b c bc b c b bc c ( b bcc) bbcc b c R + + b b + c c + b bc c b c = ( + b + c) bbcc = 589 b 0 ( b) b = ( b) b ( b) b ( b) b ( b)b ( b)b = =

221 = = 59 y z y z = k y z y y y z = k 6 6 ( ) ( y ) z k y z 6 6 k 6 k y z 6 59 b c b c b c bsic = R = sic = c R = c bc = bc = b = bc b b = c b b c c b c b c b c 0 b c = + b + c + k 6

222 + b + c + = S + = S t b + = S t c + = S t t t t = 0 ( ) (b ) (c ) = ( S t ) ( S t ) ( S t ) b c = s = (t t t ) S 595 b c b b c c c = S b = S t b c = S t S 0 t S S S + t t 0 (0 ) f() = ( )[ ] 0 0 0

223 ( )( )( ) ( ) f() = ( + )( )( ) ( ) 5 7 f( + ) + + = = f( ) ( + )( + ) ( + ) + ( + ) f() 0 f() f() = f() 5 y = k( k) y = ( ) k y = y = y = 85 k ( )[ ( ) ]log ( ) A B ( + )

224 ( + ) 600 y z = = y z y z ( ) + ( 5) + = y ( ) + y ( 5) + y (*) y ( * ) ( y) ( ) y () y =

225 log ( ) = log ( ) = lg(+ ) lg lg( + ) lg lg( ) 0 lg( ) 0 lg( ) lg() = lg( ) lg() = lg( ) 0 lg( ) lg( ) log ( ) log ( ) 60 b ( ) y = y = b = y = 5 = y = b ( ) 87 y = + b A( ) B( b = 5 5 ) b = = 5 b = log 0 0 log (log)

226 log 0 (log) 8log b c R + b b + c c + b c ( 88) + b b + c + c + = BC + CD + AB AD = ( + b + c) + y + ( ) + y + + ( y ) + ( ) + ( y) ( OP BP ) ( CP AP ) ( OB AC ) = 607 b + + b b 0) C(0 ) AC = + BC = + b AB = b

227 f() f(0) f( ) f() f( ) = b c f() = b c f(0) = c f( ) + f() f( 0) = b = f( ) f( ) c = f(0) b = [ ] f() [ ] b = [ ] f( ) = c c b b b b b = f() f( ) b b b f( ) = f() m{ f( ) f() f( ) }

228 f(0) f( ) f() 608 b = 0 b = y 0 0y0f( 0) g(y 0 ) yf() g(y)

229 = () () + y + y y + yz + z + z + z y + y y yz + z z z + () 9 + y + y = ycos0+ y () 9 y + y = ycos60+ y AB = BC = CA = y z y + y yz + z z + 6 y R + y = ( )( ) 9 y

230 b = y = b R + ( )( + b + b + b + b ( + b) b ) = = = y y y b b b ( + b + b ) + b b + b b = = 9 b b b ( )( ) 9 y y 60 w 0 ( = y = w y ( y w 0 w y 0 w w = 0 w = 65 y z R + y z = y z π AA (0 ) = A B AD AA = A C A C A C = cos y = cos z = cos = y z cos cos cos

231 = A + A + A B + AD + AA B + AD + AA B + AD + AA A B A D A A = + ( A + A + ( A + A ) + ( A + A D B A B A D ) ) A B A D A B A A A D A A = 9 A D A B A A A B A A AD = = = AB A D A B AA A D A A = = r = y = z = β + y + = 9 z () f( ) f( ) f( ) 0 0 f( ) 0 (*) 6 0 (*) (i) 0 (iii) b = 0 b = R 0 0 l ( 0 ) b ( 0 ) = 0 b = R ( b 0 0 )

232 0 + ( 0 + ) ( 0 + ) 0 R R = R ( 0 + ) ( ) = 5 R = 0 = ± b = b = 5 0 b = b = 5 = b = ( b ) = ± ( 0) ( 0) ( 5 0) ( 7 0) z = iy z = [ ] y = lg = ( 6 5 ( ) ) y = lg[( ) ] = lg

233 + + = y = = = P + + = p + = + + = ( + ) p = 0(P = P = ) = + + (P = P = ) = + +

234 60 { } d 0 0 S = lims = = d ( ) (i = ) i i+ i i+ S = d [( ) ( ) ( )] = d ( ) + + lims = lim ( ) = d + d d i= i i = { } q q = = k 5 = = (k )d k k 7 k k k = = 6 { } = S = S + S = S = S S S S = S = = S + 5 S = S = S = S = ( N ) +

235 ( ) { } S = ( ) [ ] + ( )( ) = ( ) ( + ) q p p+ q q p+q ) f() = d d = q p ( p + q) q p+ q p p q p + q q = ( ) q p = p+q = (000 ) f() = d d = ( + 9 ) S9 8 = 8 9 = 5 = S = ( + ) ( 5 + ) ( + 0) = = = 0 = 5 C = S = =

236 lim S = = S = ( + ) lim = lim S = = = S m = Am + Bm = 0 Sm = Am + Bm = 00 6lim[ + + L+ ( )( ) ] = 7 + = [ ] ( k + )( k ) k k L+ 7 ( )( + ) = [( ) + ( ) + L+ ( 7 )] + = [ ] + lim[ ( )( ) ] + + L+ = 7 + S S = b = b M b i = i= + b

237 b S = b S N = = T + 7 b 9 9 S7 = b 9 T7 S 7 + = T = = b f() = f( ) + f( ) + L+ f( ) = = = f( ) f( ) c = m b c y (m b)y b = 0 c = b m 0)(b b [ m 0) U (0] S+ 67 { } = q 0 lim S S+ + lim = lim = S

238 + S+ q () q = S q + q q q q = q q q + q 0 q q lim S (0 q ) + = S q (q ) (p + q)(sp S q ) S p+q = p q = 0 d S p q = p + q S p q = p + q ± S

239 S p+ + k p+ k p + + k ( p + )( Sp p) ( p ) k p = ( p )( p + + k) S p+ + k p+ k k p + + k S S = = p + k S S = = p + k p + ( p S S ) S p + k p k p + k ( p k S S ) S p + k p k ( p + k)( S p k p) ( p k) p = ( p k)( p + k ) ( p + )( Sp p) ( p ) k p ( p )( p + k) ( p + k)( S p k p) ( p k) p = Sp = p ( p k)( p + k ) ( S r S r ) ( S b ) S = S( r) + r = = r r ( S b ) = S r rs = + b S = ( )d d 6d = 0 d = = d = = + 5d = 0 9

240 + ( ) d = m m + m m d = ( ) ( m + ) d = m S m+ = m b m = b b = ( ) + b ( ) = 0 6 S { } S S S 5S S { } 5 ( S5) = SS 5 S + S = (5b) = (b)(b) ( b) (b) =

241 = 0 b = 6 = 5 b = S = S = 5 5 = = lim S = S S b q S = q = q + b ( + ) q = = b + + = q lim = lim = 0 S ( + r ) q q lim = lim ( )( = S + r q ) + r q q = 0 lim S = 0 lim q 0 q lim = S + r q lim = 0 S b = + c b ( )c

242 c = b = 0 b c lim = S { } S { } lim = lim S = ( + ) 68 α α α α α α () α α α α α = = 0 α () α α α α = f() = (0 0) 5 ( = ) = ()

243 S S ) = S S = S S S S = S S = ( ) S S { } = d = S S = ( ) = S S = ( N) = S S = = ( ) + 8 ( = ) = ( ) + 8 q q = (q ) 0 0 b 0 q 0 bc ( + b + c ) b b b b 0 b b b = b ( b )b ( b b + b )

244 S = + S ( ) + ( )S = ( ) + + ( ) S ( ) ( ) [ ( ) ] + S = lg [ ( + ) ] ( ) 655 { } S b = b = S S S S5 { } S d = d 8 d = = d = ( +) S = b = ( + ) {b } b ( ) +

245 S = [( ) ( ) ( )] + = ( ) = + + b c A( ) B(b ) C(c ) y = b c A B C b c b A B C y b c d = bq d = q d = 5 d = 0 ( ) 7d = b q 7d = q q = q = = log 6 = 6 blogb = b = b = {b } S S S S b = ( + ) {b }( ) q =

246 b = S = b 8 q b S = b + b + L+ b + L= b + = 8 (lgs lgs + ) lgs + S S +S +S ( qs ) ( qs )S (S + + S S+S + (lgs lgs + ) lgs = ( + ) + ( ) + = ( ) ( N) = 0 k ( k + ) = k k 0 = k k+ [ ] + = ( ) k ( +) k { } + ( = ( ) + () ( ) () ( ) k

247 k+ = k ( ) k = k + + [( ) ] ( + ) = + ( ) = ( ) + 0 ( ) + ( ) k () ( )( ) ( ) + () ( )( ) ( ) + () A = ( )( ) ( ) = 6 L 5 B = 5 7 L A A B A = ()( ) ( ) + () A = ( )( ) ( ) = 5 8 L 7 5

248 C = 7 6 B = 0 9 L L + + = + = + = + + = + A A BC = ( )( ) ( ) + ( +) + = ( + ) + + = M = ( + ) M( ) = 80( ) M M = { } S = S ( ) S = { } S = S S S = + = + ( ) ( ) S = S + ( ) = S S = = + + ( ) ( ) ( )

249 b c b c 667 N L+ k k k + = = ( + ) k + + k + k + + k k L f() log ( ) ( ) () b f () S = b b b S ( ) () ( ) ( ) [() ]( ) 0 ( ) ( + ) ( ) () b = f () ( ) = ( ) ( ) ( ) ( ) ( ) ( ) = ( ) ( ) = ( ) ( ) = ( ) ( ) = ( )

250 ( ) ( ) S ( ) S = C + C + L + ( + ) C 0 SC + C + L + ( + ) C 0 S ( )C ()C C k C = C k ( k = L ) 0 S ()C ()C ( )C 0 = ()(C + C + L+C ) ( ) S ( ) m m () m { } m m+ ( N) ( + ) + + () = = + ( ) ( N ) + f() [f()] mi f() = + ( N) f() = = N + + [f()] = f() = mi 0 0 m m + (m N) m 0 (0 ) m + m 0 m m+ m +

251 q = b + d d = = = + b d b = bq ( ) d = [ ( ) d ] ( )( ) d ] ( )! [ ( ) d ] π 67 { } = lg00si lg 5 d = lg 0 ( ) 5 = lg 5 0 = lg S 8 lg ( + ) A = = ( + ) B = ( ) =

252 0 = C b C b d C b d C b d m m C C C 0 ( ) C d C b C b d C b d C b d d b = C b d b d b d C b C b C b d 0 = = L ( + ) =

253 () Q = ( 5 ) = 5 Q = ( 5 ) = Q = ( 5 ) = 5 6 ( ) 6 Q = ( 5 ) 5 5 ( ) ( ) Q = ( 5 ( 5 ) ) = (5 ) [(5 ) ] 5 () Q0 5 5 ( ) 0 [( ) ] N = ( 5 ) lgn = 0lg 5 0 = 0( lg) = 0( 0.9) = { } = = = = = = = = = = 5 5 { L} = [ ( ) ] = ( 7)

254 = ( 7) B C B AC = ( A C ) (S -S ) S = - B = A + C B AC = ( A + C ) AC = ( A C ) ( ) { } = log ( )( 0 ) S b { } S log b + ( ) log b + = log + S = log [( )( ) ( )] S log b + ( )( ) ( ) + f() = + ( + )( + ) L ( + ) ( + )( + ) L( + ) f( + ) + + = f( ) ( + )( + ) L( + ) + = +( + ) + = + ( + ) + ( +) + + = = = ( + ) + ( + ) + ( + ) +

255 f() = = ( )( + + ) L( + ) + = 9 +7 = { } = 5 b = 5 b = () i= i S = ()d S = + = ( ) d k 0 k 00 0 k (k N) k = 7 i = S 7( 8 9 ) i= 7 = ( 7 ) ( 8 ) = 6

256 () 95 = 0 d = + 6d = + 9d = 8 ()S = ( )d = ( ) = 5 6 S 68 { } = lg 60 S lg lg60 + lg lg S = f() = lg60 + lg lg60 + lg lg f() = 0 = 0 = = lg 68 = ( ) = Nb = 9 + +

257 b = 9 = 9 = 5 b = 9[ ( ) ] + [ ( ) ] = [( ) ] 0 ( ) b 0 ( ) b b = 5 c = ( ) c y = ( ) ( 97) = ( ) = 9 6 = ( ) = A(0 ) C(0 ) B(0 ) C(0 ) 6 6 AC = 9 6 = 6 = = = 5 BC 6 6 = = b b = L+ +

258 k () k k+(k = ) k+ + + L + + ( ) + = ( ) k k+ k+ + + L + p + ( p) [( ) + ( ) + L+ ( ) + ] = p L+ + p + ( p) + p + = 686 b = ( r)q r = q = log 9. b + log b log b + log [( + r) q ] = log b log [( + r) q ] log ( + r) + log q = log ( + r) + ( )log q = + 0. c = log b+ c = + c = log b N = S + () = = S = 0 =

259 + = = S = ( + ) = 0 + = = S = ( + + ) = = 6 0 = 0 k + = S k S k = k k+ + = S k+ = ( Sk + k+ ) ( + 0 ) 0 S = + 50

260 lgs + lgs+ () lgs + lg( S c) + lg( S+ c) = lg( S+ c) lg( S c) + lg( S+ c) = lg( S+ c) S S + S + = c(ss + S +) ( S c)( S c) ( S c) = S S +S + 0 lg( S c) + lg( S+ c) = lg( S+ c)

261 ( ) ( ) ( ) = ( )( ) + = ( )( + ) ( ) ) = ( )( + ) = ( ) ( )( + ) ( + ) = L+ ( N) = k k = k k ( k + ) ( k + ) + + L+ y d y yq y q d + + d + y = 7 y = 7 y = = y

262 r = AB C r = ( ) + ( ) = + k () AC (c )(k = 0 ) BC k b (c b)(k = 0 ) AB k k S = [ (c ) b (cb)]( k ) k=0 = + b c b ( k ) k( k ) k=0 k=0

263 = ( )( )( b) ( )( )(c b) = ( )( )( b c) 6 α π ) 0 A B C S ABC α = π = y cos y cos = y cos 0 0 α0 0 α y 0 = π siα si y = si α 0 = 0 ( siα cosα = ( siαcos α) = si( α π ) 6 = 0 si( α + π ) ( 0 ) = S + + ( ) si( α π = = + ) si ( α + π S ) 6 6

264 {S } S si ( α + π ) 6 0 α π π α π π 6 6 si ( α π + ) 6 S S = = si ( α + π ) 6 S = S S = S ABC 0 = si ( α + π ) 6 S = S 0 ABC S ABC S ABC si ( α + π ) = 6 si ( α + π ) 6 si( α π ) = 6 θ α π π α = ( ) () S = lg ( + ) [ + ( )

265 S = lg ( ) [ + ( ) ] + ( ) S = lg + [ + ( ) ( + + )] (+ ) bk+ ( k + ) b k k = = ( + ) k (+ ) (+ ) k k k k m ( ) b = + = b b + + = b b = b b b b = b + b { b } b = = = b b b = 9 9 b = + ( )( ) = ( ) ( + ) b =

266 = b = ( + ) b ( + ) = ( ) = = 8 = 6 = (d)q = = ( d)q = 8 = ( d)q = dq = 8 6 = d = q = = d = q = = k kk k S = L S = L ( ) + +

267 S = k k + + LL+ = k k k = d d ( + )(i ) i i+ i i+ k k k = ( ) = = d d i= i i+ k k + = = + + L+ = + + L+ = + + L+ = = = k = 5 = = =

268 ( ) 5 5 = = = 5 = = = 0) ( + + ) ( + + ) = ( +

269 A B C D 5 70 z = i i rgz 5π π π π A B C D 6 z = i i = i π π rgz C z = bi z = b bi z R b = 0 π 705 i A i B + i + C + i D + i π i π Aθ B πθ π π C θ D θ

270 6 8 π θ( π) B π π π π θ ( π) θ (0 ) π 5π θ( π ) A B C5 D A i B i C i D i z = z A 5 B 6 C 7 D 8 6 z = z

271 7 z = z z = z = ( + i) 70 5 ( i) A i B i C i D i ( i) ( i) 5 π A C D A i B ± ± i C + i D ± ± i ( ± i ) = i i i ( i) ± = i [ i( ± i)] = i ( i ) ± = i D 7 z = cos isi (0 ) = π (z) + z = π rg θ =

272 θ θ ω = ( z) = cos + i si + z + cosθ + isiθ si θ + i siθcosθ = cos θ + isiθcosθ = t θ(siθ + icos θ) = t = π 7π π π t θ = θ = = (cos isi ) 6 6 rg = π π 6 π π tθ = 5 θ = = + (cos π i 6 si π 6 ) rg = 6 π π π 7π θ = 7 z rg(z z) = 5 π z = 0 z = zz = (bi) (bi) = bi rg(zz) = 5 b 5 = t π = = b z = 0 ( ) b = 0 = = 8 / 5 b = b = 9 / z = i z = i 0 b 0 z = i

273 z = + i z = i 75 z = siθicos θ( π θ π) z z z = si icos si 0 π cosθ 0 α (0 ) π cosθ si( θ ) π θ t α = = = t( ) siθ π + cos( θ ) π π π θ π θ π 0 α = π θ 76 z z z = z z = z z = k ( z z ) ( z z ) ( z k k + z ) k+ ZZ = zz =

274 OZ M OM = Z M = t Z OM = MZ = MO z z = cos0 isi0 = w = cos0 isi0 = w z z ( z z ) k z z k+ k+ + ( ) + ( ) = 0 z z z 77 z R z wz = 0 w = z z z ( z) z R = ( ) = z z z z z z z z z z = ± i w = z z z w = ± i = rgw = ( ± i) = π π 78 z R z = z z z R z (z ) (z z z ) = 0 (z z)( z ) = 0 z z = z z = () z = z z R z 0 z = z = ( ) z = i z = z = i

275 79 f(z) = z z f( z) = 0 i z = ( (- ) + y ) yi = 0 i ( ) + y = 0 y = = 5 z = 5 i y = z z = + z = z = i (z z ) = i z = z = + i z + z = i 7 z = cos + isi u cos isi z u + i 5 5 z u (z u)(zu) = (zu)(z z + u ) (z + u) = zu 7 ( + i) = + i si( ) cos( ) = t( ) = si( α β) = cos( α + β) 7

276 7 z = i + ( i) z = = + i 997 z z z = + i = = 998 = = + = + i z ( z ) z = z z z = z z = z z z OZ OZ z z = z z z z z z 7 75 = rgz = rgz rgz = z z 6 8 rg z + z z z z = z z z z z z z z z z z z (cos + isi )

277 z = z (cos 6 + isi 6 ) 7 7 z z (cos + isi ) 8 8 z + z z z (cos + isi + cos + i si ) = z (cos + isi ) 8 8 z rg z + i + + i = z 7 7 cos + i si 8 8 z + cos + isi 6 = z 7 7 cos + isi 8 8 z = [cos( ) + isi( )] z 8 8 z + 6 = [cos( ) + isi( )] z z = z 8 76 z = i z i z si icos z z i z 9 5 z ( + i) = (cos + isi ) 6 6 z ( i) = [cos( ) + isi( )] z cos isi = cos( ) + i si( ) 9 i = i 8 icos + i si z (cos si )( ) [cos( ) si( )] z + i + i = i z 5 5 (cos + isi )[cos( ) + isi( )]

278 5 = [cos( + ) + i si( )] = (cos + i si ) = Z bi = ( bi)(cos + si ) ( ) ( i) bi = ( bi)( + i) ( i) ( b ) ( b )i = 0 b = 0 b = 0 = + 6 b = 6 z = + + ( ) i 6 6 z 78 z (z )(z = z z = z +

279 z z z z = z (z )(z ) z z z z z z 0 0 z + bi z bi ( )( + ) + b = 0 ( + ) + b = b = z = i z z ( + z = 0 zz z z + z + z + z z z = z z z z z = z z z z z R = = z z z z z = z (z z )(z + zz + z ) 0 z + z z + z = 0 z z ( ) + + = 0 z z z = i z 7 z C z iz = z =

280 z iz z iz z z = + i (z )(z z z z z = i z + 7 z z z + = () = z bi( b R) = 0 b 0 () () 0 () i R (5) = i( R 0) z + + i ( R 0) z + = zi iz = ( i ) z + i z = = ( i ) 7 z z z = + + z z z z + z + z z = z = z

281 z z = z z = z z = z z z = = = z z z + + z z z z + z + z ( z + z + z) + + = z z z = = z + z + z z + z + z 9 0iz z = z bi b R z + 0i 9 0iz + 0b + 0 ( + b ) z = = z + 0i ( + b ) + 0b y R z i z = y ( y)i rg z z + z 0 = ( ) z z z rg z z z = = i z z i z z z rg z z z z = i z z i = i [ y ( y) i]i ( ) i = (y ) ( y )i = y = y = y = +

282 z = ( ) + ( + )i z = ( + ) + ( )i z + z ( ) = ( + i) = ( i) = = = i i y + y yi y + y y = 0 = + (0) 0 ( + ) ii 0 y z = ( )i z ( )i iii ( + ) ( )i ( + )i ( + ) 78 z t i( ) z t i( ) = si + i cos = (si + icos ) cos = ( )( si i cos ) cos

283 = ( )[ cos( ) i si( )] cos = ( )[cos( ) + isi( )] cos ( + ) + ( + ) + ( + ) t = t + 70 t z t i t t + t C t t + bi(b R b 0 t ) t ( + bi) t = (t ) + bi z t i t = z ( i) z ( i) = (z z 6 i) z O ( ) (0 ) (6 ) ( 0 ) O ( ) 6 O OM O M O M Rt OMO

284 O M O O 6 MOO = 6 O O = (rgz) = 6 rgz mi = (cos k + isi k + ) 6 6 k 0 (cos + isi ) = i 6 6 k = = (cos + isi ) i 5 5 k = = (cos + isi ) i k = (cos + isi ) i 6 6 k 5 (cos + isi ) i k = 5 6 = (cos + isi ) = i 6 6 z

285 r = z bi + b k + z (z C) t = ( z z ) u u cos v cot uv + sec v ( 0) ( 0) t t = ( z z )

286 = 0 () b( ) = 0 () b 0 () () Z Z O( O ) Z z = i Z Z z = z [cos( ) isi( )] = + + i z = z (cos isi ) = + i ( z + z ) z + = + z ( ) = z z z + = z = z (*) z 0 76 z ()z z 0 z 0 ()z z

287 0 z R z 0 0 ( z + ) ( z + ) = 0 z z ( z z) + 0( ) = 0 z z ( z z)( 0 ) = 0 zz z = z z z z () z z z R z 6 z 0 z 0 z z 0 6 z 6 z 0 z 6 zz = z 0 z 0 z (z ) z z 6 z (*) z 0 (z ) z z z z 0z z z z w i = i(wi) wi = wi (w + i)(wi) = (w + i)(w + i) (wi)(wi) 7 w i

288 + i z = i t + 79 z itt C z t t + t + t t t + + t = 0 ( t t t t + )( )( + )( ) = 0 ( t )( t ) ( tt 9) = 0 ( t )( t ) z it t = z ( i) z ( i) = t = t z ( i) z 6 i z i z M P( i) r = M (6 i) M ( i) z ()( z z z ) ( N ) (z z )(z z ) (z z )(z z ) z z zz + z z = 0 + ( ) = 0 z z z z

289 ( z z ) z () = mi(m R m 0) k k (k N) z ( z z ) R k (k N) k (k 0 ) 75 z = i w = + i zw z w ( ) z ( i) i w = ( + i) = z w z w zw z w = = = i zw zw zw z w z w = zw 75 z C zz iz = i iz z i i ()(i) ( i) i + i () i i ( )i ( N ) i( + i) () = [(i) ] [( i) ] i + i S = ( +)i = i i 75 t z = cos t + si ti r r z cos t + si t i

290 z = cost + sit z = cost sit cost z r si + t = k k 0 f(k) = = = k 0 f(k) = = = ( + ) = k k + f(k) = = = = = k k ( k k ) f( k) = k k + ( k) k ( k ) 756 z w = z w z () u = z u + z w = z z z

291 z w w i () z = ( w ) w + ( ) = w w z ( ) () u = z = u z + z + u u w u u w u = R u u w + u u z z z + u w ()w u w w + = (w ) w + w u ( w + ) w = 0 w + = z z = z = zz = + i OABC z z OC z AOB rg z BOC = rg z z z z z z z z rg rg z z z z = + i = (cos + i si ) 6 6 z z rg = = z 6 z z z z = zz = z z z z rg = rg = z z z z z 6

292 = z z si AOB z z si BOC = si 8si = z = ( i) ( + i) 0 z = ( i) ( + ( ) ) ( + ) () z = = ( + ( ) ) ( + 6) = ( + ) = ( 0 ) = ( i) ( + i) () z = ( i)

293 = ( + i)( + i) 6 ( i) + i = ( + i)( ) i + + = ( + )[ ( i )( i i ) ( i)( + i) ] = ( + i)( i) = ( + i) rgz = 760 M {z zz iz iz 5 z C} = m = y y = m = O O ( ) = 5 76 z i z = rgz [ ] z + z