In Trigonometry Formulas, we will learn

Shifting angle by π/2, π, 3π/2 (CoFunction Identities or Periodicity Identities)
 Inverse Trigonometry Substitutions
Basic Formulas
sin, cos tan at 0, 30, 45, 60 degrees
Pythagorean Identities
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
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 (EvenOdd 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 (CoFunction 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
Double Angle Formulas
Triple Angle Formulas
Half Angle Identities (Power reducing formulas)
Sum Identities (Sum to Product Identities)
Product Identities (Product to Sum Identities)
Product to sum identities are
2 cosx cosy = cos (x + y) + cos(x  y)
2 sinx siny = cos (x + y)  cos(x  y)
2 sinx cosy = sin (x + y) + sin(x  y)
2 cosx siny = sin (x + y)  sin(x  y)
Law of sine
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
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 Substitution
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