keltirish formulalari

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15.08.2023

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Trigonometrik funksiyalarini ishoralari
y = sin x
y
x y = cos x
y
x y = tg x, y = ctg x
y
x+
+ +
+ + +
  
   
 
 
  V  V  V

Choragini belgilang 273
 96
  120
     



2



2



2
3



23
 273
 96
  120
     



2



2



2
3



2
3

ctg =sin =6

3 tg 45 ° =cos 60 ° =
cos 135 ° = ?21
2
1
1
3 3
6

3

2
1
2
1
3
3

Keltirish formulalari

- Buformulalari har qanday burchakning
trigonometrik funktsiyalarining qiymatlarini
birinchi chorak burchagi funktsiyalari bo'yicha
ifodalashga imkon beradigan formulalar, ya'ni.
<90 °.0
90  
0
90  

QOIDA 1. agar burchak OY o'qidan qo’yilgan ??????
bo'lsa, unda funksiya nomi o'xshashga o'zgaradi
   2
0
xy
0
2
I II
III IV
   
   2
2
III
III IV
   

QOIDA 1. agar burchak OY o'qidan ??????
qo’yilgan bo'lsa, unda funksiya nomi
o'xshashga o'zgaradi



2
0
xy
0
2
3
I II
III IV
2




2
3
  cos sin 
  ctg tg 



2
2
3
III
III IV
2




2
3
  cos sin 
  ctg tg 

Qoida 2. Formulaning o'ng tomonidagi belgi
chap tomonidagi funktsiya belgisi bilan
aniqlanadi
0
xy
02 
    2sin  sin 
 
  sin  sin 
 
  tg  tg
      2 cos  cos
I II
III IV
 
  2ctg  ctg 
2 
      2 sin  sin 
      sin  sin
      tg  tg
      2 cos  cos
I
II
III IV
      2 ctg 
ctg

Qoida 2. Formulaning o'ng tomonidagi belgi
chap tomonidagi funktsiya belgisi bilan
aniqlanadi.2
3
0
xy
0
I II
III IV
2
 







2sin

cos








23
cos
 sin 








2tg
 ctg 
 tg  





 

2
3
ctg
2
3
III
III IV
2
 







2sin

cos
 





 

2
3
cos  sin 
 





 

2
tg 
ctg
 tg  





 

2
3
ctg

Keltirish formulalarini yozib oling 
 
090sin
    
0 180 cos
    
0 270 tg
    
0 270 sin
    
0 90 cos
    
0
360 sin
 cos
 cos 
 ctg
 cos 

sin

sin
    
0
90 sin
    
0
180 cos
    
0
270 tg
    
0
270 sin
    
0
90 cos
    
0
360 sin
 cos
 cos 
 ctg
 cos 
 sin 
 sin 

Masala 1. Trigonometrik funktsiyalarni
45 ° kichik burchak bilan ifodalang.

168 sin  
 12 sin 12 180 sin  

123cos
   33 sin 33 90 cos   

174tg
   
 969 cos
   6 6 180 tg tg   

263tg
   7 7 270 ctg tg  
 
 20 20 360 ctg ctg      
 
380ctg
 
 31 sin 31 270 cos   
 168 sin  
  
12 sin 12 180 sin  

 123 cos  
  
33 sin 33 90 cos   


174 tg
   

969 cos
 
  
66180 tgtg 


263 tg  
  
77270 ctgtg 
 
  
20 20 360 ctg ctg        

380 ctg
 
  
31sin31270cos 

Masala 2. Ifodani soddalshtiring      
 
180sin90cos360cos3cos3    
        sin sin cos 3 cos 3
2 sin α
      
   180sin90cos360cos3cos3
   
        sin sin cos 3 cos 3

Masala 3. Ifodaning qiymatini toping :
2 2

cos 135° = cos (90 ° + 45°)
cos(180° - 45°) = - sin 45°
- cos 45 °II
=
sin
34
=
 






3
π
3
3 π
sin  






3
π
sin 

3
sin -

2
3
- III
2
2

3
4 






3π
33 π
sin
 






3
π
sin 

3
sin -

2
3
-

Masala 4 (В7). Ifodani soddalshtiring
sin 150 ° · tg225° =  
 )45 tg(18030 180sin
    tg45 sin30
  1
2
1
=
=
2
1 = 0,5
          ) 45 tg(180 30 180 sin
    tg45 sin30
  1
2
1
2
1

Masala 4 (В7). Ifodani soddalshtiring
sin 150 ° · tg225° =  
 )45 tg(18030 180sin
 tg45 sin30
 1
21
=
=
2
1 = 0,5
   )45 - tg(27060 sin 90
 tg45c cos60
 1
21
=
2
1 = 0,5=
          ) 45 tg(180 30 180 sin
    tg45 sin30  1
2
1
2
1
         ) 45 - tg(270 60 sin 90
    tg45 c cos60  1
2
1
2
1

Birlik aylana х    V у R = 1

Trigonometrik funksiyalarini ishoralari y = sin x y x y = cos x y x y = tg x, y = ctg x y x+ + + + + +              V  V  V

Choragini belgilang 273  96   120          2    2    2 3    23  273  96   120          2    2    2 3    2 3

ctg =sin =6  3 tg 45 ° =cos 60 ° = cos 135 ° = ?21 2 1 1 3 3 6  3  2 1 2 1 3 3

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