1. Introduction to triginometric ratios

Trigonometry (originated from the Greek word tri means three, gon means sides and, metron means measure) is a branch of mathematics that deals with the study of relationships involving the length of sides and angles of triangles.

Consider a right-angled triangle with a corresponding angle \(\theta\).

 

 

In the figure, the side opposite to the given angle \(\theta\) is called the 'Opposite side', the side adjacent to the given angle \(\theta\) is called the 'Adjacent side', and the greatest side opposite to right angle is called the 'hypotenuse'.

 

 

Based on the corresponding angle \(\theta\), we will learn about three basic trigonometric ratios satisfied by a right-angled triangle.

 

Each of these ratios is obtained by dividing one side of the right-angled triangle by another.

 

The three basic trigonometric ratios are:

 

 

The table below depicts the relation of these ratios with the right-angled triangle.

 

Name of the angle	Sine	Cosine	Tangent
Short form of the angle	\(\sin\)	\(\cos\)	\(\tan\)
Measurements related to the right-angled triangle
Relationship	\(\sin \theta\) \(=\) \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)	\(\cos \theta\) \(=\) \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)	\(\tan \theta\) \(=\) \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)