math formulas

List of Trigonometry Formulas PDF

Trigonometry formulas are a set of different formulas containing trigonometric identities used to solve problems based on the sides and angles of a right-angled triangle. In our article, we will list the trigonometry formulas. We will see trigonometric identities. You will also be able to download these formulas in PDF form.

List of Trigonometry Formulas

Basic Trigonometry Formulas

Basic Trigonometry Formulas Trigonometric Ratio Formulas

Trigonometric Ratio Formulas

  • sin θ = Perpendicular/Hypotenuse
  • cos θ = Base/Hypotenuse
  • tan θ = Perpendicular/Base
  • sec θ = Hypotenuse/Base
  • cosec θ = Hypotenuse/Perpendicular
  • cot θ = Base/Perpendicular

Trigonometry Formulas Involving 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

Signs of Trigonometric Functions

Signs of Trigonometric Functions

The Law of Sines

the law of sines

Sine Area Formula

(sin A)/a = (sin B)/b = (sin C)/c

sine area formula

The Law of Cosines

  • a= b+ c– 2bc cosA
  • b= a+ c– 2ac cosB
  • c= a+ b 2ab cosC

The Law of Cosines

Trigonometry Formulas Involving Sum and Difference Identities

 

Trigonometry Formulas Involving Sum and Difference Identities

Trigonometry Formulas Involving Double Angle Identities

Trigonometry Formulas Involving Double Angle Identities.jpg

Trigonometry Formulas Involving Half-Angle Identities

sin (x/2) = ±√[(1 – cos x)/2]

cos (x/2) = ± √[(1 + cos x)/2]

tan (x/2) = ±√[(1 – cos x)/(1 + cos x)]

or, tan (x/2) = ±√[(1 – cos x)(1 – cos x)/(1 + cos x)(1 – cos x)]

tan (x/2) = ±√[(1 – cos x)2/(1 – cos2x)]

⇒ tan (x/2) = (1 – cos x)/sin x

Trigonometry Formulas Involving Sum to Product Identities

Trigonometry Formulas Involving Sum to Product Identities

Trigonometry Formulas Involving Product Identities

Trigonometry Formulas Involving Product Identities

Trigonometry Formulas Involving Periodic Identities(in Radians)

 

First Quadrant:

  • sin (π/2 – θ) = cos θ
  • cos (π/2 – θ) = sin θ
  • sin (π/2 + θ) = cos θ
  • cos (π/2 + θ) = – sin θ

Second Quadrant:

  • sin (3π/2 – θ) = – cos θ
  • cos (3π/2 – θ) = – sin θ
  • sin (3π/2 + θ) = – cos θ
  • cos (3π/2 + θ) = sin θ

Third Quadrant:

  • sin (π – θ) = sin θ
  • cos (π – θ) = – cos θ
  • sin (π + θ) = – sin θ
  • cos (π + θ) = – cos θ

Fourth Quadrant:

  • sin (2π – θ) = – sin θ
  • cos (2π – θ) = cos θ
  • sin (2π + θ) = sin θ
  • cos (2π + θ) = cos θ

Trigonometry Formulas Involving Co-function Identities(in Degrees)

  • sin(90° − x) = cos x
  • cos(90° − x) = sin x
  • tan(90° − x) = cot x
  • cot(90° − x) = tan x
  • sec(90° − x) = cosec x
  • cosec(90° − x) = sec x

Trigonometry Formulas Involving 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 (-x) = -sin-1 x
  • cos-1 (-x) = π – cos-1 x
  • tan-1 (-x) = -tan-1 x
  • cosec-1 (-x) = -cosec-1 x
  • sec-1 (-x) = π – sec-1 x
  • cot-1 (-x) = π – cot-1 x

Trigonometry Formulas Involving Triple Angle Identities

  • sin 3x = 3sin x – 4sin3x
  • cos 3x = 4cos3x – 3cos x
  • tan 3x = [3tanx – tan3x]/[1 – 3tan2x]

 

Trigonometric Ratio Table

Trigonometric Ratio Table

 

Download trigonometry formulas as pdf: Trigonometry Formulas PDF

Sorumatik

Sorumatik Web Sitesi (Uygulaması) Kurucusu.Eğitim Uzmanı ve Yazar.Öğrencilere ücretsiz yardım etmeyi hedefleyen Yazar,Eğitimci,Mühendis.

Bir cevap yazın

E-posta hesabınız yayımlanmayacak.

Başa dön tuşu