Microsoft Word Formula kitobcha

Trigonometrik tengsizliklar

^{x }^{arcSina  2nπ ;π  arcSina  2nπ}  ^{;
x }^{π  arcSina  2nπ ;arcSina  2nπ}  ^;

3. 
   Cosx  a
   
4. 
   Cosx  a
   

_ a  1_ , 
_ a  1_ , 
^{x }^{arcCosa  2nπ ;arcCosa  2nπ} ^{;
x }^{arcCosa  2nπ ;2π  arcCosa  2nπ}  ^;

5. 
   tgx  a
   

^{a  R}^{, }
x  ^arctga  nπ ; ^π  nπ ^ ;


_{ 2} 

6. 
   tgx  a
   

^{a  R}^{, }
x ^  ^π  nπ ;arctga  nπ ^ ;

 _{2 }
 

7. 
   ctgx  a
   

^{a  R} ^{, 
x }^{nπ ;
arcctga  nπ} ^;

8. 
   ctgx  a
   

^{a  R} ^{, 
x }^{arcctga  nπ ;
nπ}  ^{. (Bu yerda n  Z .)}

Ba’zi trigonometrik ayniyatlar

1. sin x sin(60  x)sin(60  x)  ¹ sin 3x .
4
2. 16Sin10⁰ Sin30⁰ Sin50⁰ Sin70⁰ Sin90⁰  1.
3. 16Cos80⁰Cos60⁰ Cos40⁰Cos20⁰Cos0⁰  1.
4. 16Sin20⁰ Sin40⁰ Sin60⁰ Sin80⁰  3.

π C	os ^4^πC	os ^5^π	1		.
7	7	7	8
π C	os ^2^πC	os ^4^π			1
7	7	7			8
π C	os ^3^πC	os ^5^π			1
7	7	7			8

5. 16Cos10⁰ Cos30⁰Cos50⁰ Cos70⁰  3.


6. Cos

7.

Cos .

8. 
   Cos .
   

8. 
   Cos ^2π Cos ^4π Cos ^6π  ¹ .
   

7 7 7 8

8. 
   

π 3π
Cos Cos
  ¹ .

5 5 4

8. 
   

Cos^π  Cos ^3π  ¹ .

5 5 2

8. 
   

Sin ^π
4n
Sin ^3π
4n
Sin ^5π
4n
     Sin ^{(2n 1)π}  ² .
4n 2ⁿ

8. 
   

Cosx  Cos2x  Cos4x  ... Cos2ⁿ
x  ¹ 
₂n1
Sin2^n1 x
.
Sinx

_Sin nx _Cos (n  1)x

8. 
   

Cosx  Cos2x  ...  Cosnx 
2 2 _.
Sin ^x
2

Teskari trigonometrik funksiyalar orasidagi bog‘lanishlar

arcSinx  arcCosx  ^π ; arctgx  arcctgx  ^π
2 2

1. 
   arcSin( x)  arcSinx; arcCos( x)  π  arcCosx .
   
2. 
   arctg(x)  arctgx;arcctg(x)  π  arcctgx .
   

3. 
   arcSinx  ^π
   

2

4. 
   arcCosx  ^π
   

2

• 
  arcCosx  arctg ^x .
  

• 
  arcSinx  arcctg ^x .
  

5. 
   arctgx  ^π
   

2

• 
  arcctgx  arcSin ^x
  

6. 
   arcctgx  ^π
   

2

• 
  arctgx  arcCos ^x .
  

Trigonometrik va teskari trigonometrik funksiyalar orasidagi bog‘lanishlar

^{1. Sin}^arcSinx ^{ x ,
x }^1;1^{. 2.}
arcSin(Sinx)  x , x  ^ ^π ; ^{π } .

_ _{2 2} _

^{3. Cos} ^arcCosx ^{ x ,
x }^1;1^{. 4.}
arcCos(Cosx)  x ,
^{x }^0;π ^.

5. arctg(tgx)  x,
x ^  ^π ; ^{π } . 6. tg(arctgx)  x,


x  R .

 _{2 2} 
 

7. arcctg(ctgx)  x,
^{x }^0;π  ^{. 8.}
ctg(arcctgx)  x,
x  R .

^{9. Sin}^arcCosx ^{
, x }^1;1^{. 10. Cos} ^arcSinx ^{
1  x2 , x }^1;1^.

11.

13.
^Sin^arctgx <sup>


Sin</sup>^arcctgx  ^{
x . 12. Cos} ^arctgx ^{ 1 .
1 . 14. Cos} ^arcctgx  ^{ x .}

^{15. tg} ^arcSinx <sup>


17. tg</sup> ^arcSinx ^{
x , x }^1;1^{. 16. tg} ^arcSinx ^{
x , x }^1;1^{. 18. tg} ^arcSinx ^{
x , x }^1;1^{,
x , x }^1;1^.

19.

^Sin^arcctgx ^
1 . 20.
^Sin^arcctgx ^{ 1 .}

Teskari trigonometrik funksiyalar yig‘indisi

1. 
   arcSinx  arcSiny  arcCosx(
   

2. 
   arcSinx  arcSiny  arcCosx(
   

3. 
   arcSinx  arcSiny  arcCosx(
   

4. 
   arcSinx  arcSiny  arcCosx(
   




^arcCos _xy 

5. 
   
   
   arcCosx  arcCosy 
   

^arcCos xy 


• 
  xy) .
  

• 
  xy) .
  

• 
  xy) .
  

• 
  xy) .
  







_, x  y,
_, x  y.

6. 
   arctgx  arctgy  arctg
   

x  y _,
1  xy


xy  1.

7. 
   arctgx  arctgy  arctg
   

x  y _,
1  xy


xy  1.

8. 
   arcctgx  arcctgy  arcctg ^{xy ∓ 1} , x   y .
   

x  y

Funksiya va uning asosiy xossalari

X sonlar to‘plamidan olingan x ning har bir qiymatiga biror qonuniyat yoki qoida yordamida Y sonlar to‘plamidan olingan yagona y qiymat mos kelsa, bunday

moslik funksiya deyiladi va
y  f (x)
ko‘rinishida belgilanadi.

X to‘plam funksiyaning aniqlanish sohasi deyiladi va belgilanadi.
Y to‘plam esa funksiyaning qiymatlari to‘plami deyiladi va
belgilanadi.