Trigonometric Formulas

Trigonometric Formulas With Table

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)30°45°60°90°180°270°360°
Angles (In Radians)0π/6π/4π/3π/2π3π/2
sin01/21/√2√3/210-10
cos1√3/21/√21/20-101
tan01/√31√300
cot√311/√300
cosec2√22/√31-1
sec12/√3√22-11

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

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Ahsa.Pk

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This Post Has 2 Comments

  1. Haziq

    Please add chapter 12 and 13 formulae

    1. Ahsa.Pk

      They will also be added there in a short while.
      Thanks for attention.

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