حساب المثلثات 1 ث ترم اول
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Transcript of حساب المثلثات 1 ث ترم اول
(( )) / / 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 <