( ) Well. . . . cot( ) is the evil twin of tan( ). ( ) Imagine a small child coming down from the slide. ( ) Greater the slope. . . greater the value of tan( ). {Actually tan( ) = slope = dy/dx = rate of change of y w.r.t x } ( ) Greater the value of tan( ), . . .greater the velocity of the kid. ( ) Thus, velocity of the kid in a way = directly proportional to tan( ). ( ) Now greater the slope the kid. . . .the lesser the chances of the kid landing smoothly. So probability of a smooth landing is inversely proportional to tan( ). ( ) But instead of writing 1/ tan ( ) . . . again and again in equations . . . .mathematicians wanted something more simpler. So they invented a function cot( ) = 1/tan( ). ( ) At least it comes in the numerator . ( ) Now we can simply write, Probability of safe landing of the kid is directly proportional to cot( ) INSTEAD OF WRITING THAT.... Probability of safe landing is inversely proportional to tan( ) . . .everywhere. . . . again and again. SIMILARLY FOR COSEC( ) AND SEC( ) ( ) Cosec ( ) is the evil twin of Sin( ). ( ) Sin( ) in itself is a measure of how much perpendicular two forces/objects/influences/fields are. ( ) Whenever any event involving two things takes place such that the more perpendicular they are the greater the impact.......SIN( ) comes into picture. Now perhaps you get why SIN(90) = maximum. ( ) For example, the impact of a ball on a cardboard wall will be max at 90 degree. ( ) So,...one can write. Impact = proportional to SIN( ). ( ) So the chances of = inversely proportional to how the wall standing perpendicular the ball is to the wall. = inversely proportional to SIN( ) SO INSTEAD OF WRITING 1/SIN( ) EVERYWHERE AND TO SAVE THE MESS.... THEY(MATHEMATICIAN) GAVE BIRTH TO COSEC( ). ( ) So now they could write, Chances of the cardboard = proportional to COSEC( ). wall standing. NEAT, ISN'T IT? ..............Binnoy |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| THE ABOVE IS A EXCERPT FROM A BOOK AVAILABLE FOR PURCHASE (5$) AT THE FOLLOWING LINK VISUALIZING MATHS.PDF AVAILABLE FOR PURCHASE FOR 5$ (INR 300) HERE (PDF) |||||||||||||||||||||||||||||||||||||||||||||| DONATION SECTION DONATIONS SECTION HERE |||||||||||||||||||||||||||||||||||||||||||||||||| ABOUT I hardly understood Math in school. In fact was on the verge of dropping the subject I loved the most because as much as I loved the theory of it, I could not understand the math involved in it. However I loved the subject too much to be able to live without. Hopelessly, I was continuing my love-affair with it. Then one day....a miracle happened,....while applying a certain formula again and again.....I came to know its significance. Slowly and steadily....other equations also started clicking. I got to see a strong relationship between Maths and the Physics it was pointing towards. They both were the same. Maths was just an easy language to express a physical phenomenon. And a bit more to that in the sense that it could even predict the behaviour of a certain physical phenomenon. Equations now as if came to life. Every equation now had as if something to say. A burning urge to share these things with the world aflamed within me. So that no one has to give up the subject that he or she loves the most. The book on visualizing maths thus got written as a sprout of inspiration. The blog followed. Both these are dedicated to you and all such similar minds searching for answers. Visualizing Math & Physics is a blog dedicated to you and all such similar minds searching for answers. |||||||||||||||||||||||||||||||||||||||||||||| CONTACT [email protected] ||||||||||||||||||||||||||||||||||||||||||||||