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February 13th, 2016, 04:21 PM  #1 
Newbie Joined: Jan 2016 From: United States Posts: 14 Thanks: 1  Conceptual Understanding of Trigonometry
I'm currently taking Calculus I in highschool. As I started to read a bit about the derivatives of trigonometric functions, I made the realization that I have no idea what the significance of sec, csc, and cot, or even tan for that matter, is. I understand that they are reciprocal functions, and that tan is the ratio of the sin to the cos, but why do we even have these? Why are they their own dedicated functions? Could anyone recommend a book/resource that will help me a develop a conceptual and thorough understanding of all things trigonometry? Thanks 
February 13th, 2016, 05:18 PM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
I don't think you need a book... What you do need is to play with the graphs of these functions a bit. Then you'll realise why, for example, differentiating sin x gets you cos x. 
February 14th, 2016, 05:27 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond 
Convenience, if nothing else. All trigonometric functions can be written in terms of sine and/or cosine.

February 15th, 2016, 09:53 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
A right triangle has three sides, a, b, and c, say. There are 3 ways to take them 2 at a time: ab, ac, and bc. Including different orders, there are 6: ab, ac, ba, ca, ab, and ba. "sine", "cosine", "secant", "cosecant", "tangent", and "cotangent". That is, those functions are all the different ways of comparing pairs of sides of a right triangle.

February 27th, 2016, 08:05 PM  #5 
Senior Member Joined: Nov 2015 From: United States of America Posts: 198 Thanks: 25 Math Focus: Calculus and Physics 
If you're still looking for a book, I highly recommend the good old "PreCalculus for Dummies". They even have a Trigonometry for dummies, but I never got that one. The PreCalculus for Dummies book has a good amount of Trig in it, and proved to be very helpful to me in the past and still today!


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