# Introduction to Basics of Trigonometry # 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 right-angled 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 right-angled 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 right-angled triangles.

1. ### 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
1. ### 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(u-v) = tan(u) − tan(v)/1+tan(u) tan(v)

1. Let us assume that A, B, C are the angles & a,b,c the sides of the right-angled 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