# Trigonometric Ratios & Proves

Some Important points before we start our proves .

1. We should know the naming of sides of a right angle triangle click here to understand it .
2. Pythagoras Theorem “In a Right angled Triangle square of Hypotenuse will be SUM of square of each other sides  .” i.e Hypotenuse2 =Base2+Perpendicular2

If we take 3-4 right angle triangles having same angle ϑ that means there all triangles having a common angle and then if we calculate the ratios of sides for each different triangles like perpendicular/Hypotenuse , Base/Hypotenuse and perpendicular/base and inverse of all these .

Then we will find that each same ratios from different triangles in respect to common angle ϑ are same .

So we can easily assume that for each triangle perpendicular/Hypotenuse , Base/Hypotenuse and perpendicular/base are same in respect with angle ϑ.

So we can assume any constant for such values and which will depends on ϑ.

Mathematicians assumes SIN as Ratio of perpendicular/Hypotenuse then

Sin ϑ= perpendicular/Hypotenuse and in similar way they assumes Cosϑ=Base/Hypotenuse  and tanϑ=perpendicular/base

So we have ;

Sin ϑ= perpendicular/Hypotenuse

Cosϑ=Base/Hypotenuse

tanϑ=perpendicular/base

Inverse of Above Ratios:

Cosecϑ= Hypotenuse/perpendicular

secϑ=Hypotenuse/Base

tanϑ=base/perpendicular

To-remember these value we use a name :

pandit badri prasad har har bole and to represent these all trigonometric ratios we can arrange this like below