In Engineering and Technology formula plays main role, because without formulas no feature studies possible in science and technology. Formula is a compressed way of expressing information in symbols, as in a mathematical formula or a science formula. In this article some IMP Formula are listed below.
Factorization and Expansion
This list of formulas are use when we want to factorized some variable or to expand variables.
- a2 – b2 = (a + b) (a – b)
- a2 + b2 = (a + b)2 – 2ab
- a3 – b3 = (a – b) (a2 + ab + b2)
- a3 + b3 = (a + b) (a2 – ab + b2)
- a4 – b4 = (a2 – b2 ) ( a2 + b2 )
- (a + b)2 = a2 + 2ab + b2
- (a − b)2 = a2 − 2ab + b2
- (a + b)3 =a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – b3 – 3ab(a – b)
- (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
- (a − b)4 = a4 − 4a3b + 6a2b2 − 4ab3 + b4
- (a + b + c)2 = a2 + b2 +c2 + 2ab + 2ac + 2bc
Trigonometry IMP Formula
Basic Trigonometric Function Formula
By using a right-angled triangle as a reference, we can find all trigonometry term values.
- sin θ = Opposite Side/Hypotenuse
- cos θ = Adjacent Side/Hypotenuse
- tan θ = Opposite Side/Adjacent Side
- cot θ = Adjacent Side/Opposite Side
- sec θ = Hypotenuse/Adjacent Side
- cosec θ = Hypotenuse/Opposite Side
Reciprocal Identities
- cosec θ = 1/sin θ
- sec θ = 1/cos θ
- cot θ = 1/tan θ
- sin θ = 1/cosec θ
- cos θ = 1/sec θ
- tan θ = 1/cot θ
Trigonometry Table
Angles (In Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
Angles (In Radians) | 0° | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |
sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |
cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1 | 0 | 1 |
tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |
cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |
csc | ∞ | 2 | √2 | 2/√3 | 1 | ∞ | -1 | ∞ |
sec | 1 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | 1 |
Periodicity Identities (in Radians) formulas
These IMP formula are used to shift the angles by θ
sin (π/2 – A) = cos A & cos (π/2 – A) = sin A
sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A
sin (3π/2 – A) = – cos A & cos (3π/2 – A) = – sin A
sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A
sin (π – A) = sin A & cos (π – A) = – cos A
sin (π + A) = – sin A & cos (π + A) = – cos A
sin (2π – A) = – sin A & cos (2π – A) = cos A
sin (2π + A) = sin A & cos (2π + A) = cos A
Co-function Identities (in Degrees) formulas
- sin (90°−x) = cos x
- cos (90°−x) = sin x
- tan (90°−x) = cot x
- cot (90°−x) = tan x
- sec (90°−x) = csc x
- csc (90°−x) = sec x
Sum & Difference Identities
- sin (x+y) = sin(x) cos(y) + cos(x) sin(y)
- cos (x+y) = cos(x) cos(y) – sin(x) sin(y)
- tan (x+y) = (tan x + tan y) / (1−tan x •tan y)
- sin (x–y) = sin(x) cos(y) – cos(x) sin(y)
- cos (x–y) = cos(x) cos(y) + sin(x) sin(y)
- tan (x−y) = (tan x–tan y) / (1+tan x • tan y)
Double Angle Identities
sin (2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)]
cos (2x) = cos2(x)– sin2(x) = [(1-tan2 x)/(1+tan2 x)]
cos (2x) = 2cos2(x) − 1 = 1–2sin2(x)
tan (2x) = [2tan(x)] / [1−tan2(x)]
sec (2x) = sec2 x / (2-sec2 x)
csc (2x) = (sec x. csc x)/2
Triple Angle Identities
- sin 3x = 3sin x – 4sin3x
- cos 3x = 4cos3x-3cos x
- tan 3x = [3tanx-tan3x] / [1-3tan2x]
IMP Formula PDF
Below list of IMP Formula can Download in PDF form
- Law of Indices
- Logic of Power and Roots
- Law of Logarithams
- Factorization
- Expansion
- Trigonometry
- Trigonometry Factorization
- Trigonometry Identities
- De-Factorization
- Addition Formulae
- Trigonometry Ratio of Negative angle
- Double angle Formula
- Triple angle Formula
- Derivatives
- Integration
Basic Formulas
Integration
Derivatives
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