In Trigonometry Formulas, we will learn

 

Basic Formulas

What are sin cos tan? - SOHCAHTOA - With Examples - Teachoo - Finding sin cos tan

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sin, cos tan at 0, 30, 45, 60 degrees

Trigonometry Formulas - Part 2

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Pythagorean Identities

Trigonometry Formulas - Part 3

Signs of sin, cos, tan in different quadrants

To learn sign of sin, cos, tan in different quadrants,

we remember

A dd → S ugar → T o → C offee

 

Trigonometry Formulas - Part 4

 

Representing as a table

 

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

sin

+

+

cos

+

tan

+

+

 

Radians

Radian measure = π/180  ×  Degree measure

 

Also,

1 Degree = 60 minutes

i.e. 1° = 60’

 

1 Minute = 60 seconds

i.e. 1’ = 60’’

Negative angles (Even-Odd Identities)

sin (–x) = – sin x

cos (–x) = cos x

tan (–x) = – tan x

sec (–x) = sec x

cosec (–x) = – cosec x

cot (–x) = – cot x

 

Value of sin, cos, tan repeats after 2π

sin (2π + x) = sin x

cos (2π + x) = cos x

tan (2π + x) = tan x

Shifting angle by π/2, π,  3π/2 (Co-Function Identities or Periodicity Identities)

   

sin (π/2 – x) = cos x

cos (π/2 – x) = sin x

sin (π/2 + x) = cos x

cos (π/2 + x) = – sin x

sin (3π/2 – x)  = – cos x

cos (3π/2 – x)  = – sin x

sin (3π/2 + x) = – cos x

cos (3π/2 + x) = sin x

sin (π – x) = sin x

cos (π – x) = – cos x

sin (π + x) = – sin x

cos (π + x) = – cos x

sin (2π – x) = – sin x

cos (2π – x) = cos x

sin (2π + x) = sin x

cos (2π + x) = cos x

Angle sum and difference identities

Trigonometry Formulas - Part 5

Double Angle Formulas

Trigonometry Formulas - Part 6

Triple Angle Formulas

Trigonometry Formulas - Part 7

Half Angle Identities (Power reducing formulas)

Trigonometry Formulas - Part 8

Sum Identities (Sum to Product Identities)

Trigonometry Formulas - Part 9

Product Identities (Product to Sum Identities)

Product to sum identities are

  2 cos⁡x  cos⁡y = cos⁡ (x + y) + cos⁡(x - y)

  -2 sin⁡x  sin⁡y = cos⁡ (x + y) - cos⁡(x - y)

  2 sin⁡x  cos⁡y = sin⁡ (x + y) + sin⁡(x - y)

  2 cos⁡x  sin⁡y = sin⁡ (x + y) - sin⁡(x - y)

Law of sine

Trigonometry Formulas - Part 10

Here

  • A, B, C are vertices of Δ ABC
  • a is side opposite to A i.e. BC
  • b is side opposite to B i.e. AC
  • c is side opposite to C i.e. AB

Law of cosine

Just like Sine Law, we have cosine Law

Trigonometry Formulas - Part 11

What are Inverse Trigonometric Functions

If sin θ = x

Then putting sin on the right side

  θ = sin -1 x

  sin -1 x = θ

 

So, inverse of sin is an angle.

 

Similarly, inverse of all the trigonometry function is angle.

 

Note : Here angle is measured in radians, not degrees.

 

So, we have

  sin -1 x

  cos -1 x

  tan -1 x

  cosec -1 x

  sec -1 x

  tan -1 x

Domain and Range of Inverse Trigonometric Functions

 

Domain

Range

sin -1

[–1, 1]

[-π/2,π/2] 

cos -1

[–1, 1]

[0,π] 

tan -1

R

(-π/2,π/2)

cosec -1

R – (–1, 1)

[π/2,π/2] - {0}

sec -1

R – (–1, 1)

[0,π]-{π/2}

cot -1

R

(0,π)

 

Inverse Trigonometry Formulas

Some formulae for Inverse Trigonometry are

sin –1 (–x) = – sin -1 x

cos –1 (–x) = π – sin -1 x

tan –1 (–x) = – tan -1 x

cosec –1 (–x) = – cosec -1 x

sec –1 (–x) = – sec -1 x

cot –1 (–x) = π – cot -1 x

 

Trigonometry Formulas - Part 12

Trigonometry Formulas - Part 13

Inverse Trigonometry Substitution

 

Trigonometry Formulas - Part 14

  1. Chapter 3 Class 11 Trigonometric Functions (Term 2)
  2. Concept wise

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.