In Trigonometry Formulas, we will learn

 

Basic Formulas

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

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

Trigonometry Table.jpg

Pythagorean Identities

trigonometric identities.jpg.png

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

 

sin cos  tan in different quadrants.jpg

 

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

Angle sum and difference formulas.jpg

Double Angle Formulas

Double angle formulas.jpg

Triple Angle Formulas

Triple angle formulas 1.jpg

Half Angle Identities (Power reducing formulas)

Half angle formulas.jpg

Sum Identities (Sum to Product Identities)

Sum Identities (Sum to Product Identities).jpg

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

Sine Law.jpg

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

Cosine law.jpg

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

 

Inverse Trigonometry Formula - 2.jpg

Inverse Trigonometry Formula - 3.jpg

Inverse Trigonometry Substitution

 

Inverse Trigonometry substitution table - teachoo.jpg

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Concept wise

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.