الجدع مشترك علمي - المغرب -

1. http://ad2math.voila.net/ adnanemath@gmail.com ‫ط‬ ‫أآ‬ ‫ن‬ .‫ذ‬ Page 1
‫ا‬‫ا‬ ‫ب‬ ‫ـ‬–‫ء‬ ‫ا‬1
‫ا‬1:‫أ‬‫ا‬ ‫ول‬ ‫ا‬:
‫ر‬ ‫او‬ ‫ا‬ ‫س‬260°60°
‫ن‬ ‫اد‬ ‫او‬ ‫ا‬ ‫س‬
3
rad
8
π5
rad
6
π
‫س‬‫اد‬ ‫او‬ ‫ا‬50 grd24 grd
‫ا‬2:
1(‫ا‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫ا‬A‫و‬B‫و‬C‫و‬D‫و‬E‫ا‬ ‫ا‬ ‫ا‬ ‫أ‬ ‫ا‬:
9
4
π
‫و‬
3
π
‫و‬
6
π−
‫و‬
4
5
π
−‫و‬
38
5
π
.
2(‫ا‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫ا‬Mk‫ه‬ ‫ا‬ ‫أ‬ ‫ا‬k
6 4
π π
+k ∈».
3(‫ا‬ ‫ة‬ ‫ا‬ ‫ا‬‫ا‬ ‫ن‬‫ل‬ ‫ا‬
9
I 4 ;
2
π
π
 
=   
‫ل‬ ‫ا‬ ‫ا‬ ‫ن‬
4 17
J ;
3 4
π π 
=   
‫ا‬ ،K I J= ∩.
‫ا‬3:
1(‫ا‬ ‫ا‬ ‫ل‬ ‫ا‬ ‫د‬A‫ا‬ ‫ل‬ ‫ا‬ ‫ذات‬
34
5
π
.
2(‫ل‬ ‫ا‬ ‫ا‬ ‫ل‬ ‫ا‬ ‫د‬B‫ا‬ ‫ل‬ ‫ا‬ ‫ذات‬
954
8
π
−.
3(‫ا‬ ‫ا‬ ‫ل‬ ‫ا‬ ‫د‬C‫ا‬ ‫ل‬ ‫ا‬ ‫ذات‬
2013
3
π
.
‫ا‬4:‫ه‬ ، ‫ا‬ ‫ت‬ ‫ا‬ ‫آ‬x‫و‬y‫ا‬ ‫أ‬:
12
x
7
π
=‫و‬
2
y
7
π−
=,,,
8
x
3
π
=‫و‬
2
y
3
π−
=,,,
43
x
12
π−
=‫و‬
2
y
12
π−
=,,,
11
x
17
π
=‫و‬
6
y
17
π−
=
‫ا‬5:
‫ا‬ ‫وا‬ ‫ا‬ ‫زاو‬ ‫ا‬ ‫س‬ ‫ا‬ ‫د‬ ‫ا‬:
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
AB;AC ;; AB;AE ;; AB;AD ;; BC;AE
DA;BA ;; BD;BA ;; AE;AD ;; AE;DA
‫ا‬6:‫او‬ ‫ا‬ ‫س‬ ‫د‬α‫آ‬‫ا‬ ‫ت‬ ‫ا‬:
1(
2
sin
2
α =‫و‬
2
π
< α < π.
2(
3
sin
2
α =‫و‬
2
π
< α < π.
3(
3
cos
2
α = −‫و‬
2
π
−π < α < −.
4(tan 1α = −‫و‬0
2
π
− < α <.
‫ا‬7:‫أ‬:
25 163 125 170 7
sin ; tan ; cos ; sin ; cos
3 4 6 3 6
π π π π π         
− −         
         
.
‫ا‬8:
1(
2
tan
5
α = −‫و‬;
2 2
π π 
α∈ −  
‫أ‬ ،sin α‫و‬cosα.
2(tan 2 3α = −‫و‬0; ;
2 2
π π   
α∈ ∪ π      
‫أ‬ ،sin α‫و‬cosα.
3(
12
cos
13
α = −‫و‬;
2
π 
α∈ π  
‫أ‬ ،sin α‫و‬tan α.

2. http://ad2math.voila.net/ adnanemath@gmail.com ‫ط‬ ‫أآ‬ ‫ن‬ .‫ذ‬ Page 2
‫ا‬9:
1(
7
sin cos
5
α + α =‫أ‬ ،sin α‫و‬cosα.
2(2
2sin 5cos 4 0α + α − =‫و‬[ [0;α∈ π‫أ‬ ،sin α‫و‬cosα.
‫ا‬01:‫أن‬:
6 2
cos
12 4
π + 
= 
 
،sin
12
π 
 
 
‫و‬tan
12
π 
 
 
‫و‬
7
cos
12
π 
 
 
‫و‬
7
sin
12
π 
 
 
‫و‬
7
tan
12
π 
 
 
‫و‬
11
sin
12
π 
 
 
‫و‬
13
tan
12
π 
− 
 
‫و‬
145
sin
12
π 
 
 
‫و‬
85
tan
12
π 
− 
 
.
‫ا‬11:‫أ‬:
2 2 2 2
2 2 2 2 2 2
3 5 7
A cos cos cos cos
8 8 8 8
3 5 7 9 11
B sin sin sin sin sin sin
12 12 12 12 12 12
2 3 4
C 1 sin sin sin sin
5 5 5 5
π π π π       
= + + +       
       
π π π π π π           
= + + + + +           
           
π π π π       
= + + + +      
       
8 9
... sin sin
5 5
π π   
+ + +    
   
‫ا‬21::
2 4
2 4
x k ;k
2
sin x sin x
D
cos x cos x
π
≠ + π ∈
−
=
−
»( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
6 6 4 4 2 2
4 4 6 6
6 6 2 2
E cos x sin x cos x sin x 5sin x cos x
F 3sin x 3cos x 2sin x 2cos x
G sin x cos x 3sin x cos x
= + + + + ×
= + − −
= + + ×
‫ا‬31:
‫ا‬،ABC‫ا‬ ‫وي‬A،H‫ـ‬ ‫دي‬ ‫ا‬ ‫ا‬A
(BC).
:BAH = α‫و‬AH h=‫و‬AB a=‫و‬BC b=.
1(‫أآ‬cosα‫و‬sin α‫و‬( )sin 2αa‫و‬b‫و‬h.
2(‫أن‬ ‫ا‬:sin(2 ) 2sin cosα = α× α.
3(‫أ‬-‫رة‬ ‫إ‬ ‫أدرس‬( )cos 2α‫ا‬:0
4
π
≤ α ≤‫و‬
4 2
π π
≤ α ≤.
‫ب‬-‫رة‬ ‫إ‬ ‫أدرس‬2
2cos 1α −‫ـ‬0
4
π
≤ α ≤‫و‬
4 2
π π
≤ α ≤
‫ج‬-‫أن‬:( ) 2
cos 2 2cos 1α = α −.
‫د‬-‫ـ‬ ‫ا‬ ‫ا‬ ‫أ‬:
12
π
‫و‬
8
π
.
‫ا‬14:ABC‫و‬ ،‫دة‬ ‫زوا‬H‫ا‬‫ـ‬ ‫دي‬ ‫ا‬B(AC).
1(‫أن‬:2 2 2
BC AB AC 2AH AC= + − ×.
2(‫أن‬ ‫ا‬:( )2 2 2
BC AB AC 2AB AC cos BAC= + − × ×.
3(‫ت‬:EFG:EGF
3
π
=‫و‬FG = 4‫و‬EG = 3،‫أ‬EF.