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


Trignometry

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:

Triangle

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


Different Types of Triangles?


Equilateral triangleisoscelesScalene
rignt-triangleacuteobtuse

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.

opposite

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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