152
وى ن ا ث ل ا ول الأ ف ص ل ا ول ى الأ س الدرا ل ص ف ل ا(( ساب ح اب! ث ض ا! ري ل ا)) اب ث ل ث م ل ا ة س مدر/ م! ي ك ح ل دا ث ع ر ص ن ب! ي ق ن ل دا! ث ه ش ل ا م مب س ا ق/ ام م@ ىا ف ن ح د! ث س اذ ث س اعداذ الأ س ح1 / ى ف ن ح ث! د س ا ث! اب ض ا! ري ل ىا ف ث! د س ل اE ن س حام م@ ا

حساب المثلثات 1 ث ترم اول

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(( )) / / 1 /

2 /

: :

3

/

4 /

(< ) (< )

5

/

(< ) (< )

6 /

- - (2) ( ) - - 7 /

(1) 5 1/ = 06 // 1 5 = 06 / 1 5 = 0063 //8 /

(2) (1 )

= 9 /

=

=

01 /

=

01 4

= 5,2

01 4 /

=

=

11

5,1 5,7

5,7 = = = 5 5,121 /

4,1 01

= 4,1 5 = 7 31 /

=

( = ) 1 41 /

(2) = 08151 /

= 081

(1) 5 = 081

021

= = 021 = 2 3 081 081 02161

Sh

Exp /

081

=

,,,

6,0 6,0 081 6.071

5 =

081

/

Sh

Exp

=

,,,

081 81 /

= 2

5

= 09 /

081 2

=

91

051 5

5 602

=

= 051 081

/

5 8

5 = 52,1 4

52,1 081 = /

= =

12

56 = 4 5

5

= 2 56 = 031 = 45 5

= 031 = 3,2 081 = = 3,2 4 = 2,9 22 /

[1] 8 5

32

/

[ 2] ( )

[ 3 ] 42 /

[4] 4 [5] 6,1 01 52 /

2,1

[6] 5,1 41

62

/

[] [2] 6,1 [1] 7,0 [4] 6,4 [3] 3,2 [5] 1,5 72 /

[] [2] 071 5 [1] 011 5 [3] 04 / 051 5 [4] 52 / 0325 [5] 51// 04 / 002582 /

(1) 9 6 (2) 051 01 92 /

(3) 521 5 (4) 56 6 03 /

(5) 52 / 07 02

(6) 13 /

(7) (8) 2 323 /

[] (3) 5 (2) (1) 4 6 5 (6) 333

(5) 6 5 /

(4) 3 7

[] :5

(2) 531 (4) 033 5 (6) 513 543 /

(1) (3) 522 5 (5) 042 5

0125

)1( )2( 53 /

= 063 = ( ) 263 /

= + 063 = ( ) + 273 /

55

(1) 051/

= 051 - 063= - 0125

001

(2) 04

5

=04 / 001 5 063 = 02 / 952 5 /

83

5

05 / 002//

//

(3) 52

05 / 002 5 0635

52

= =

951

/

9

//

53

93

/

(1) 3 = 2

5= 304

3

6 = 3 /

= 5 2 4

(2) 5 4

= 5 8 = 3 4 4 /

14

[ ] (2) 512 5 (1) 031 5 (4) 02 / 001 5 (3) 003 (6) 53 / 561 5 (5) 51 / 331 5 (7)52 // 04 / 521 5 (8) 04 // 53 / 55 5 (9) 05 // 03 / 51224 /

[ ] 3 4 6

5 4 3

734

5 6 /

[ ] (2) - 542 5 (1) - 041 5 (4) - 02 / 051 5 (3) - 803 5 (5) - 54 / 731 5 (6) - 53 / 571 5 (7) - 52 // 54 / 523 5 (8) - 04 // 55 / 001 5 (9) - 02 // 03 / 572544 /

[ ] 3 4 6

5 4 3

754

5 6 /

1- ................ 2- .......... 64 /

3- ............ 4- 0031 5 ..............5- 0001 5 ..............74 /

5

(063 2 ) = + 063 5 ( )

= + 2 ( )84 /

94 /

081 05 /

09

063 0

072

0 < < 09 09 < < 081 081 < < 072 072 < < 063 15 /

5

(1) 0021

0021 = 0021 063 = 048 063 = 084 063 = 021 5 0021 5 25 /

5

(2) 0051

0051 = - 0051 +063= - 0411 +063 = - 087 +063 = - 024 +063 = -06 = -06 +063 = 003 5 0051 5 35 /

71

3

71 71 081 = 0211 = 3 3 = 0211 063 = 067 063 = 004 063 = 04 71 345 /

55

/

(01) (-1 0 )(1 0 )

( 0 -1 )65 /

(0 0 ) =(01) = (1 0 ) = ( 0 -1) = (-1 0)75 /

() 1

=() ( ) /

85

) sin() 1

(1) ( = =

( ) = = 95 /

)cos() 1

(2) ( = =

( ) = =06 /

) tan() 1

(3) ( = =

= 16

( ) = /

(4) ( )() 1

= =

1

1 =

1 1 ( ) = = 26 /

(5) ( )() 1

1 = = = 1

1

1 36

( ) = = /

(6) ( )() 1

= = =

1

46

( ) = = /

=1

2

+

2

() 1

56

/

= = ( ) () 1

1

=

=

1

= =

=

66

=

/

( ) () 1

)

3 2

1 2

(

3

2 = 3

= 21 = 3 / 76

2 = 1 2

=

= 3

( ) () 1

(1) ( 1 ) > 0 2

(2) = ( 6.0 8.0 ) (3) ( ) < 0 /

(4) = ( 1 0 )86

( ) () 1

(1) = ( 2 ) < 0 3 (2) = ( 6.0 ) > 0

(3) = ( 1 )(4) = ( 3 4 ) > 0

96

/

( ) +

+

07 /

(1) ( ) ( ) () ( ) ( ) +

+

+ + +

+

+

17

/

(2) ( ) ( ) () ( ) ( )+

+

+ + +

+

+

27

/

(3) ( ) ( ) () ( ) ( )

+

+

+ + +

+

+

37

/

(4) ( ) ( ) () ( ) ( )

+ +

+ +

+ + +

47

/

(1) ( ) ( ) ( ) (2) () ( ) ( ) (3) ( ) ( )57 /

( )

001 ( ) 001

001 ( ) 001 001 ( ) 001 67 /

(1) 051 .............. (2) 001 ............... (3) 003 .............. (4) 522 .............. (5) 033 ............ (6) 06 ...............77 /

(7) 05 .............. (8) 012 ............... (9) 041 .............. (01) 031 .............. (11) 032 ............ (21) 071 ...............87 /

(31) 002 .............. (41) 07 ............... (51) 0052 .............. (61) 523 .............. (71) 061 ............ (81) 042 .............97 /

(91) 013 .............. (02) 023 ............... (12) 08 .............. (22) 57 .............. (32) 03 ............ (42) 003 ...............08 /

(52) (-001) ............ (62) (-003) ........... (72) (-051) ............ (82) (-03) ........... (92) (-002) ............ (03) (-0002) ...........18 /

(13) (-003) ............ (23) (-0001) ........... (33) (0001) ............ (43) (0002) ........... (53) > 0 < 0 .................28 /

(63) > 0 > 0 ................. (73) < 0 < 0 ................. (83) < 0 > 0 .................

38

/

5

541 2

5

0612

5

03

5

063

5

072

5

081

5

09

0

1)2

3) (2 3 2

(1 0) (0 1 ) (-1 0) (0 -1) (1 0) ( 3 1 ) (22

1 2

1 23 2 1 3

0 1 0

10

0 10

1 0

0 1 0

1 2 148

1 2

3

/

(1) 06 03 + 06 03 1 1 3 3 = + 2 2 2 2 4 1 3 = + = = 1 4 4 458 /

(2) 2 54 + 54 - 081 + 1 ( 1 ))2

1 2 1

= (

+ 1 +1 = 5,268 /

2

=

(1) 09 = 2 54 54 = 09 = 1 1 1 1 = 2 = 2 = 1 2 2 2 78 /

03 06 + 54 09 +2081= 1 = 2 + 1 1 +2 ( 1 ) 2 = 1 + 1 2 = 2 2 = 88 /

0 5 < < 09 5 = 2 54 54 1 1 = 2 2 2 1 = 2 2 = 09 5 = 198 /

0 5 < < 09 5 = 2 06

3 = 2 2 = 3 = 06 5 09 /

0 5 < < 09 5 = 4 03 03

3 2

1 = 4 2 = 3 = 03 5

19

/

0 5 < < 09 5

= 2 09 = 2 1 = 2

= 1 25

= 03

29

/

(1) 09

( 09 ) = ( 09 ) = ( 09 ) = ( 09 ) = ( 09 ) = ( 09 ) = 39 /

= 09 = = = ....................... :- + = 09 5 (1) = + = 09 5 (2) = + = 09 5 (3) = 49 /

(7) 57 = ....... (8) 58 = ...... (9) 72 = ..... (01) 13 = ...... (11) 27 = ...... (21) 45 = ....59

(1) 05 = ..... (2) 03 = ....... (3) 07 = ........ (4) 56 = ...... (5) 08 = ..... (6) 55 = ......

/

(1) = + = ....... (2) ( 09 ) = .......... (3) = + = ...... (4) ( 09 ) = ........... (5) = + = ..... (6) 02 / 05 5 = ........69 /

= ......... (1) 04 = (2) 52 / 03 5 = ................ = .......... (3) = 2 (4) 05 / 02 5 = ............... = ......... (5) 2 = 3 (6) (09 ) = ................... = .......... (7) = (8) ( 09 ) = ............ (9) ( 09 ) = ................. (01) ( 09 ) = ............79 /

= 2 + 2 =09 5 3 = 09 = 03 5

89

/

4 = 5 4 +5 = 09 9 = 09 = 01 599 /

( +02) = ( + 05) +02 + +05 = 09 2 +07 = 09 2 = 09 07 2 = 02 = 01 5001 /

(+01) = ( 04 )

+01 + 04 = 09 2 03 = 09 2 = 09 +03 2 = 021 = 06 5101 /

( +04) = ( + 02) +04 + +02 = 09 2 +06 = 09 2 = 09 06 2 = 03 = 51 5201 /

(2 03 ) = ( 3 + 01) 2 03 +3 +01 = 09 5 5 02 = 09 5 = 09 +02 5 = 011 = 22 5301 /

4 5 = 1 1 4 = 5

4 = 5 4 + 5 = 09 5 9 = 09 5 = 01 5401 /

081

( 081 ) = ( 081 ) = ( 081 ) = ( 081 ) = ( 081 ) = ( 081 ) = 501 /

081

021 051 531601 /

0215

021= (081 06 ) = 06 =

32

2 021 = 3 1 021 = (081 06 ) = 06 = 2 021 = -2

021 = ( 081 06 ) = 06 = 31

3701 /

021 =

5

05112

051= (081 03 ) = 035 = 0515 = 2

3

051 5 = (081 03 ) = - 03 = - 2 051 5 = - 2 3 1 0515 = ( 081 03 ) = - 03 = 3 051 = - 3801 /

53151

531= (081 54 ) = 54= 2 531 = 21

531 = (081 54) = - 54 = 2 531 = - 2

531 = ( 081 54 ) = - 54 = - 1 531 = -1901 /

081 +

( 081 + ) = - ( 081 + ) = - ( 081 + ) = - ( 081 + ) = - ( 081 + ) = ( 081 + ) = 011 /

0125 042 5 5225042= (081 + 06 ) = - 06 = - 3 2 2 042 = - 3

042 = (081 + 06 ) = - 06= 1 2 042 = - 2

042 = ( 081 + 06 ) = 06 = 3 1 042 = 3111 /

5

541 2

5

0612

5

03

5

081 5 072 5 063

5

09

0

1)2

3) (2 3 2

(1 0) (0 1 ) (-1 0) (0 -1) (1 0) ( 3 1 ) (22

1 2

1 23 2 1 3

0

-1

0

1

0

1 2

1 2

10

0

10

0

10

1211

3

/

0125012= (081+ 03 ) = - 03 = 1 2 012= - 2 012 = (081 + 03 ) = - 03 = - 3 2 012 = - 2 3

012 = ( 081 + 03 ) = 03 = 1 3 012 = 3311 /

5225522= (081 + 54 ) = - 54= 1 2 522 = - 2 522 = (081 + 54) = 54 = 1 2 522 = - 2

522 = ( 081 + 54 ) = 54 = 1 522 = 1411 /

063

( 063 ) = - ( 063 ) = - ( 063 ) = ( 063 ) = ( 063 ) = - ( 063 ) = - 511 /

003 033 513003= (063 06 ) =- 06 = - 003 = -

003 = (063 06 ) = 06 = 003 = 2 003 = ( 063 06 ) = - 06 = - 3 003= - 611 /

00 3 033 513 033= (063 03 ) = - 03 = 033= - 2 033 = (063 03 ) = 03 = 033= 033 = ( 063 03 ) = - 03 = 033= - 3711 /

00 3 033 513 513= (063 54 ) = - 54= 513 = - 2 513 = (063 54) = 54 = 513 = 2 513 = ( 063 54 ) = - 54 = - 1 513 = -1

811

/

( ) = - ( ) = - ( ) = ( ) = ( ) = - ( ) = - 911 /

(- 03 ) = - 03 = 5,0 (-03) = 033 = (063- 03) =- 03 = 5,0 (-03) = 03 = (-03) = 033 =(063- 03) = 03= (-03) = - 03 = (-03)= 033 = (063 03) = - 03= 021 /

(-051) = - 051 = - (081 03) = - 03 = (-051) = 012 = (081+03) = - 03 = (-051) = 051 = (081 03) = - 03 = - (-051) = 012 = (081+03) = - 03 = - (-003) = - 003 = - (063 06 ) = - - 06 = 06 = ( -003 ) = 06 =121 /

(1) 051 003 + 021 012 + 531

051 = (081 03 ) = - 03 = 003 = (063 06 ) = - 06 = 021 = (081 06 ) = - 06 = 012 = (081+03) = - 03 = 531 = (081 54 ) = - 54 = - 1221 /

2 522 5 021 5 (- 003 ) 042

522 = (081 +54 ) = 54 = 1 021 = (081 06 ) = - 06 = ( - 003 ) = 06 = 042 = (081 +06 ) = - 06 =

-

= 2 1 = -1 + 1 =

321

/

[] [5,0] )1( 2522 021 ( - 003 ) 042 )2( (2) 024 033 + ( - 021 ) 012

[] [52,1]

(3) 018 (-585 ) + 576 036 (4) 012 024 513 + 09

421

/

[ 57,0] (5) ( - 06 ) 021 + 003 057 [ 5,0] (6) 522 042 ( - 003 ) 033 [ 1 ] (7) 024 ( - 096 ) + 012 042 [ ] (8) 051 024 033 003 [-1 ] (9) 069 0501 ( - 084 ) 012 (01) 033 ( - 021) + 084 ( - 06) [ ]

521

/

= = = = = =

621

/

( ) ( )

/

721

( ))2 )2 )2

( )2 = ( )2 + (

( )2 = ( )2 ( ( )2 = ( )2 (

821 /

5

3

4

(1) = ...... (2) = ..... (3) = ...... (4) = ....... (5) = ....... (6) = .......

921

/

(1) = ......... (2) = ....... (3) = ........ (4) = ........ (5) = ....... (6) = ........

5 3

4

031

/

5

= 6,0 0 5 < < 09

01 131

6

8 /

0 < < 09

2131

=

+ = 8 0 < < 09 515

+ = 4

231

/

09 5

0 <