# 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 \DeltaABC. 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)

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