All classes equally use Trigonometric Formulas for their preparation. Practice these formulas by putting different values into them.
Trigonometric Formulas
Trigonometric 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 | ∞ |
cosec | ∞ | 2 | √2 | 2/√3 | 1 | ∞ | -1 | ∞ |
sec | 1 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | 1 |
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
Inverse Trigonometry Formulas
- sin-1 (–α) = – sin-1 α
- cos-1 (–α) = π – cos-1 α = cos-1 α
- tan-1 (–α) = – tan-1 α
- cosec-1 (–α) = – cosec-1 α
- sec-1 (–α) = π – sec-1 α = sec-1 α
- cot-1 (–α) = π – cot-1 α = -cot-1α
Cofunction Formulas
- sin(90° − α) = cos α
- cos(90° − α) = sin α
- tan(90° − α) = cot α
- cot(90° − α) = tan α
- sec(90° − α) = cosec α
- cosec(90° − α) = sec α
Sum and Difference Formulas
- sin(α+β) = sinαcosβ + cosαsinβ
- sin(α-β) = sinαcosβ – cosαsinβ
- cos(α+β) = cosαcosβ – sinαsinβ
- cos(α-β) = cosαcosβ + sinαsinβ
- tan(α+β) = (tanα + tanβ) / (1 – tanαtanβ)
- tan(α+β) = (tanα – tanβ) / (1 + tanαtanβ)
Half-Angle Formulas
sinα/2 = ±√(1-cosα)/2
cosα/2 = ±√(1+cosα)/2
tanα/2 = ±√(1-cosα)/(1+cosα)
See Also: 11th Class Maths Chapter 10 New Book
Double Angle Formulas
- sin2α = 2sinαcosα
- cos2α = cos2α – sin2α = 2cos2α – 1 = 1 – 2sin2α
- tan2α = 2tanα / (1 – tan2α)
Triple Angle Formulas
- sin3α = 3sinα – 4sin3α
- cos3α = 4cos3α – 3cosα
- tan3α = 3tanα – tan3α / (1- 3tan2α)
Product to Sum Formulas
- sinα + cosβ = 2 sin(α + β)/2 . cos (α – β)/2
- sinα – cosβ = 2 cos(α + β)/2 . sin (α – β)/2
- cosα + cosβ = 2 cos(α + β)/2 . cos (α – β)/2
- cosα – cosβ = -2 sin(α + β)/2 . sin (α – β)/2
Sum to Product Formulas
- 2sinα . cosβ = sin(α + β) + sin(α – β)
- 2sinα . sinβ = cos(α – β) – cos(α + β)
- 2cosα . cosβ = cos(α + β) + cos(α – β)
1st Year Maths Trigonometric Formulas
Do You Need Concepts? Must Watch 1st Year Math Full Book Solution

Please add chapter 12 and 13 formulae
They will also be added there in a short while.
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