What is a Trigonometric ratio?

Definition

The ratio between sides of a right triangle is called a trigonometric ratio.

Introduction

In a right triangle, there are three sides and each side has some length naturally. The length of one side can be compared with the length of another side to know that how many times a side is to another side of a right-angled triangle. However, It can be done mathematically by the concept of ratio.

So, the ratio between any two sides of a right triangle can be calculated mathematically and the ratio is called a trigonometric ratio. Now, let’s clearly learn what a trigonometric ratio really is in trigonometry from a visual example.

In a right-angled triangle, the names of three edges are opposite side, adjacent side and hypotenuse, and every side has measurable length. Now, the ratio between any two sides can be calculated mathematically by division and their quotient is called a trigonometric ratio.

For example, let’s calculate the ratio of opposite side’s length to the length of adjacent side. It is calculated mathematically by division.

Likewise, there are five more ratios in trigonometry and let’s know each trigonometric ratio one after one.

List of Trigonometric Ratios

In trigonometry, there are six ways to calculate the ratio between the three sides of a right triangle. The following are the six trigonometric ratios in mathematical form.

$(1).\,\,$ $Trigonometric \, Ratio$ $\,=\,$ $\dfrac{Opposite \, side}{Hypotenuse}$

$(2).\,\,$ $Trigonometric \, Ratio$ $\,=\,$ $\dfrac{Adjacent \, side}{Hypotenuse}$

$(3).\,\,$ $Trigonometric \, Ratio$ $\,=\,$ $\dfrac{Opposite \, side}{Adjacent \, side}$

$(4).\,\,$ $Trigonometric \, Ratio$ $\,=\,$ $\dfrac{Adjacent \, side}{Opposite \, side}$

$(5).\,\,$ $Trigonometric \, Ratio$ $\,=\,$ $\dfrac{Hypotenuse}{Adjacent \, side}$

$(6).\,\,$ $Trigonometric \, Ratio$ $\,=\,$ $\dfrac{Hypotenuse}{Opposite \, side}$

Names of Trigonometric Ratios

The ratio between every two sides of a right triangle is called the trigonometric ratio but it definitely confuses us while discussing about a particular trigonometric ratio. So, a name for each trigonometric ratio helps us to know whichever trigonometric ratio we talk about. The following are the names for six trigonometric ratios.

$(1).\,\,$ $Sine$ $\,=\,$ $\dfrac{Opposite \, side}{Hypotenuse}$

$(2).\,\,$ $Cosine$ $\,=\,$ $\dfrac{Adjacent \, side}{Hypotenuse}$

$(3).\,\,$ $Tangent$ $\,=\,$ $\dfrac{Opposite \, side}{Adjacent \, side}$

$(4).\,\,$ $Cotangent$ $\,=\,$ $\dfrac{Adjacent \, side}{Opposite \, side}$

$(5).\,\,$ $Secant$ $\,=\,$ $\dfrac{Hypotenuse}{Adjacent \, side}$

$(6).\,\,$ $Cosecant$ $\,=\,$ $\dfrac{Hypotenuse}{Opposite \, side}$

Now, remember the trigonometric ratios by their names and let’s start learning the trigonometry completely.

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