# Introduction to Trigonometry

As per Wikipedia, Trigonometry (from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides.

In simple words, we can say that

## What is a Triangle?

A triangle is a basic geometric shape having three vertices, three sides (edges) and three angles.

A triangle with three vertices A,B and C as shown in this figure is commonly denoted as `\Delta`ABC. a, b, c are three sides of the
triangle whereas `\alpha ,\beta and \gamma` denote the three angles. One simple identity holds for the angles of all types of triangles:

**`\alpha + \beta + \gamma = 180^\circ`**

## Different Types of Triangles?

Among these triangles, the Right Triangle (or Right Angled Triangle) is of great importance. We see it in detail:

## Right Angled Triangle

This special type of triangle has one of the three angles equal to `90^\circ` and this angle is demonstrated by a small square inside the triangle. `\theta` can be any angle.

Note that the side of the triangle adjacent to angle `\theta` is named as adjacent (A). The side opposite to angle `\theta` is named as Opposite(O), whereas the third (longest) side is named as Hypotenuse(H).

## Trigonometric Ratios

`sin x = text(Opposite)/text(Hypotenuse)` ; cosec x = `text(Hypotenuse)/ text(Opposite)`

`cos x = text(Adjacent) / text(Hypotenuse)` ; `sec x = text(Hypotenuse) / text(Adjacent)`

`tan x = text(Opposite) / text(Adjacent) ` ; `cot x = text(Adjacent) / text(Opposite)`