Trigonometric Formulas

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)

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)

By Ahsa.Pk

We are sharing meaningful and related notes and all materials for students.

2 thoughts on “Trigonometric Formulas”

Leave a Reply

Your email address will not be published. Required fields are marked *

Don't Miss Out Anything!

Receive top education notes, lesson ideas, teaching tips, and more!

teacher

You have successfully subscribed to the newsletter

There was an error while trying to send your request. Please try again.

will use the information you provide on this form to be in touch with you and to provide updates and marketing.