 # Maths Formulas for Class 11

## Class 11 Maths Formulas

In Mathematics, formulas play an important role. In Maths, a lot of reasoning and logic is involved. This section has a class 11 maths formula list. Here are the formulas that you need to know and all of them are sectioned chapter-wise for better understanding. Having a strong grip on your formulas is important to score better in your exams. Check out these important formulas, print them out for your reference, keep them handy! They will be helpful!

### Sets Formula

A set is a collection of elements. Now, these elements can be anything. Also, it can be a finite set as well as an infinite set.

 Symbol Set N The letter N denotes a set of only natural numbers Z The letter Z denotes a set of the only integers Q The letter Q denotes a set of only rational numbers R The letter R denotes a set of only real numbers Z+ The letter Z+ denotes a set of only positive numbers Q+ The letter Z+ denotes a set of only positive rational numbers R+ The letter R+ denotes a set of only real positive numbers ∪ It is called a union ⋂ It is called an intersection

1. The union of two sets X and Y can be denoted as X ∪ Y

2. The difference or intersection of two sets X and Y as X ⋂ Y

3. The complement of X is denoted by X’

4. (i)  ( X ∪ Y )’ = X’ ⋂ Y’

(ii) ( X ⋂ Y )’ = X’ ∪ Y’

1. If (  X ⋂ Y ) = Φ,  then n( X ∪ Y ) = n(A) + n(B)

2.  (  X ∪ Y ) = Φ, then n (  X ∪ Y ) = n(A) + n(B) - n(A ⋂ B)

### Relations and Functions Formula

Formulas important in relations and functions chapter are:

1.  A x B = { (a, b) : a є A, b є  B }

2. If ( p, q ) = ( s, t ) = then p = s and q =  t.

3. If n ( X ) = a and x ( Y ) = b, then n ( X x Y ) = x * y.

4. X x Φ = Φ.

5. The cartesian product: X x Y ≠ Y x X

6. A function f ( x ) from set X to set Y has on relation type where elements of set X have only one image in Y. Therefore, f ( x ) = y or f: X ➝ Y.

7. If function f: A ➝ R and g: A ➝ R, then:

• ( f + g ) ( x ) = f ( x ) + g ( x ), x Є A

• ( f - g ) ( x ) = f ( x ) - g ( x ), x Є A

• ( f . g ) ( x ) = f ( x ) . g ( x ), x Є A

• ( k f) (x) = k (f ( x ) ),  x Є A , k is a number.

• f/g ( x ) = f(x)/g(x), x Є A , g ( x ) ≠ 0

### Trigonometric Functions Formula

1. Radius Measure = (π/180) x (Degree Measure)

2. Degree Measure = (180/π) x (Radian Measure)

3. Cos2 y + sin2 y = 1

4. 1 + tan2 y = sec2 y

5. 1 + cot2 y = cosec2 y

6. cos(2nπ + y) = cos y

7. sin(2nπ+ y) = sin y

8. sin ( π- y ) = -sin y

9. cos (π - y ) = - cos y

10. cos ( (π/2) - y ) = sin y

11. sin ( (π/2) - y ) = cos y

12. sin ( y + x )  = sin y * cos  x + sin x * cos y

13. sin ( y - x )  = sin y * cos  x - sin x * cos y

14. cos ( y + x )  = cos y * cos  x - sin x * sin y

15. cos ( y - x )  = cos y * cos  x + sin x * sin y

16. cos ( (π/2) + y ) =  - sin y

17. sin ( (π/2) + y ) =  - cos y

18. cos(π- y) = - cos y

19. sin (π - y) = sin y

20. cos(π + y) = cos y

21. sin (π + y) = - sin y

22. cos( - y) = - cos y

23. sin ( - y) = - sin y

24. tan (x + y) = (tan x + tan y)/(1 - tan x tan y)

25. tan (x - y) = (tan x - tan y)/(1 + tan x tan y)

26. cot (x + y) = (cot x cot y - 1)/(cot y - cot x)

27. cot (x - y) = (cot x cot y + 1)/(cot y - cot x)

28. Cos 2y = cos2 y - sin2 y = 2 cos2 y - 1 = 1 - 2 sin2 y =  (1 - tan2y)/(1 + tan2y)

29. sin 2y = 2 sin y : cos y =  (2 tan y) (1 + tan2y)

30. sin 3y = 3 sin y - 4 sin3 y

31. tan 3x = (3 tan x - tan3y)/(1 - 3  tan2y)

32. cos x + cos y = 2 cos (x + y)/2 cos (x - y)/2

33. cos x -  cos y =  - 2 sin (x + y)/2 sin(x - y)/2

34. sin x + sin y = 2 sin (x + y)/2 cos (x - y)/2

35. sin x - sin y = 2 cos (x + y)/2 sin (x - y)/2

36. 2 cos x cos y = cos ( x + y ) + cos ( x - y )

37. - 2 sin x sin y = cos ( x + y ) - cos ( x - y )

38. 2 sin x cos y = sin ( x + y ) + sin ( x - y )

39. 2 cos x sin y = sin ( x + y ) - sin ( x - y )

40. sin y = 0; gives y = nπ, where n Є Z

41. cos y = 0; gives y = (2n + 1) π/2, where n Є Z

42. 𝑠𝑖𝑛 𝑥 = 𝑠𝑖𝑛 𝑦; gives x = 𝑛𝜋 + ( - 1 )n y, where n Є Z

43. 𝑐𝑜𝑠 𝑥 = 𝑐𝑜𝑠 𝑦; gives 𝑥 = 2𝑛𝜋 ± 𝑦, where n Є Z

44. Tan x = tan y y; gives x = n𝜋 + y, where n Є Z