Introduction to Basics of Trigonometry
Trigonometry is one of the significant branches in the history of mathematics and this idea is given by a Greek mathematician called Hipparchus. The basics of trigonometry define three primary functions which are sine, cosine, and tangent.
Trigonometry ratios in the rightangled triangle:
These ratios are also called fractions. Sine, cosine, tangent are the most fractions and they are abbreviated as sin, cos, tan.
All of the six functions of trigonometry and their relations are as follows:
Functions  Abbreviation  Relation to a rightangled triangle 
sine  sin  Opposite side/hypotenuse 
tangent  tan  Opposite side/adjacent side 
cosine  cos  Adjacent side/hypotenuse 
cosecant  cosec  hypotenuse/ opposite side 
secant  sec  hypotenuse/adjacent side 
Cotangent  cot  Adjacent side/opposite side 
Trigonometry formulas:
There are a number of trigonometry formulas that we can use to solve problems. All of these formulas are true in the case of rightangled triangles.

Pythagorean Identities
 sin²θ + cos²θ = 1
 tan2θ + 1 = sec2θ
 cot2θ + 1 = cosec2θ
 sin 2θ = 2 sin θ cos θ
 cos 2θ = cos²θ – sin²θ
 tan 2θ = 2 tan θ / (1 – tan²θ)
 cot 2θ = (cot²θ – 1) / 2 cot θ

Sum & difference identities:
The angles are u&v
 sin(u + v) = sin(u)cos(v) + cos(u)sin(v)
 cos(u + v) = cos(u)cos(v) – sin(u)sin(v)
 tan(u+v) = tan(u) + tan(v)/1−tan(u) tan(v)
 sin(u – v) = sin(u)cos(v) – cos(u)sin(v)
 cos(u – v) = cos(u)cos(v) + sin(u)sin(v)
 tan(uv) = tan(u) − tan(v)/1+tan(u) tan(v)
 Let us assume that A, B, C are the angles & a,b,c the sides of the rightangled triangle in use. Then, the laws go like
Sine Laws
a/sinA = b/sinB = c/sinC
Cosine laws
c2 = a2 + b2 – 2ab cos C
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 – 2ac cos B
Trigonometry identities:
The three of the most important functions are as follows:
 sin²θ + cos²θ = 1
 tan²θ + 1 = sec²θ
 cot²θ + 1 = cosec²θ