Some Important points before we start our proves .
- We should know the naming of sides of a right angle triangle click here to understand it .
- 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
Inverse of Above Ratios:
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
pandit badri prasad / har har bole
If we take all words first latter then it will become
P will represent Perpendicular , B base and h Hypotenuse .
And if we take it from up to down we will have sin=>P/H , Cos=>B/H => and Tan => P/B and if we take down to up we will have all inverse ratios cosec=>H/P,Sec=>H/B and cot=>B/P.