4: R.A.T. & Trigo Ratios

There are two triangles which you must know like the back of your hands. 

1. Isosceles Right Angled Triangle
2. Equilateral Triangle


The trigonometric ratios of Sin Cos Tan 45 comes from here.

​See below.


The trigonometric ratios of angles 30 and 60 degrees come from this Equilateral triangle. It is very easy to see that 

a Cos 60 = a Sin 30 and
a Sin 60 = a Cos 30 from the above diagram

So, now we know the source of the three vital angles 45, 30 & 60 degrees and can see how the geometry leads to the trigonometry. 

Next we will place these triangles in Coordinate Geometry and look for insights. 


Become familiar with this triangle because this is one of the most commonly occurring triangle in any geometrical problem. You should be able to recognize this triangle from far away and be able to tell the three sides immediately.

A very important point is that half of a SQUARE is precisely this isosceles right angled triangle. Study the diagram below.  

Go to Lesson Five