Introduction to the three trigonometric ratios and two laws.

 Author- K .Venkataraman

Trigonometry is the study and measurement of angles and sides of a triangle. Trigon literally means 3 sides and metry means measurement. There are three main ratios of trigonometry and the other three are just functions of the first three, so let us see what are the ratios.

 

1)      Sine

2)      Cosine

3)      Tangent

 

These are the three ratios and the others are just inverses of the three

 

  

First let us see about sine.

 

Sine is the ratio between the opposite side and the hypotenuse of a right-angle triangle, here is a diagram for reference.

 

 

                                              

 

 

 

 

 

 

Table of sin values: -

 

 

 

 

 

 

 

Solved example-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cosine.

 

Cosine of an angle is the ratio between its adjacent angle and the hypotenuse., here is a diagram for reference.

 

 

Table of cosine values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 solved example:-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tangent is the ratio between the opposite side of a triangle and its adjacent side.

Here is a diagram for reference.

 

 

 

Table of tan values

  

                             From https://www.grc.nasa.gov/www/k-12/airplane/tabltan.html

 solved example:

 

 

 

 

 

 Actually, there is a mnemonic to remember all the three ratios and their functions, it is:

 

SOHCAHTOA

Here soh is sine opposite hypotenuse, cah is cosine adjacent hypotenuse, toa is tangent opposite adjacent.  So, this mnemonic will help a person in remembering the trig ratios.

Now, let us look at some trigonometric laws

 

 

Law of sines.

 

This law states that the ratio between the sine of an angle and its opposite side is constant throughout the triangle-

Diagram for reference

 

 

 

 

 

 

 

 

 

 

 

 

 

Solved examples

 

 

Law of cosines-

This law states that the third side of a triangle can be known if the other 2 sides and their enclosing angle are known. It goes like-

 

 

 

Solved example-

 

 

 I hope the reader understood these concepts.