In this blog, we are going to give you some tips and tricks regarding a really important chapter of JEE Maths — Trigonometry. My goal is to help you gain a better understanding of this chapter, as well as solving problems from it.
Let’s first talk about how important trigonometry is for the JEE (both Main and Advanced). If you check previous years’ papers, you will find that hardly 1 – 2 questions in trigonometry were asked in the JEE Main. The same goes for JEE Advanced! Yet many professors and mentors recommend studying this chapter thoroughly. But why?
The main reason is the application of trigonometry to everything else on the test. Yes! Trigonometry itself may not come up directly on the exams, but is widely used in other chapters. And this application is not limited to Maths. Trigonometry is used on a large scale in Physics as well.
Although the chapter initially seems a little boring, trust me, it isquite the opposite. It is really useful in solving the majority of problems that show up on the JEE. So, how should you prepare for trigonometry in order to use it for the majority of questions found in the JEE? I will list some reference books which I used to refer for studying or practising questions during my JEE Preparation.
Books You Should Buy for Trigonometry (or for Complete Mathematics)
- Plane Trigonometry – Book by S. L. Money
- Trigonometry by G. Tewani (by Cengage series)
- M. L. Khanna (A must for practising questions)
- Amit M. Agarwal (Arihant)
You may also go for R. D. Sharma (even if it is not at par with level of the JEE Advanced, almost every CBSE student has it for school purposes). Besides this, previous years’ papers and some practice papers should be more than enough.
Plane Trigonometry by S. L. Loney is a must-have for the JEE. It covers almost everything in trigonometry, and teaches concepts in a well defined and easy manner. Besides this, lots of new formulae are given which can be memorised (as they are not too complex) and widely used in various other parts. One of them is given below.
tan(a + b + c + …) = (S1 – S3 + S5…) / (1 – S2 + S4…) where Sn is the sum of all possible products of separate tangents (products in n) taken at the time. For example, S1 is tan(a) + tan(b) +… and so on for Sn.
Using this, we can easily calculate values of tan(2x) or any tan(nx) just by taking a = b = c = …
This probably would take a lot of time to do manually–but it can be done in a few seconds using this formula. There are lots of other surprises in this book. This was just a small example.
The Study of Trigonometry Can Be Classified into Two Parts
- Remembering important Formulae and revising them again and again.
- Practicing more and more questions using these formulae.
Doing these two things will make your concepts strong and you will excel in the subject.
Methods of Studying These Two Parts of Trigonometry
So how do you complete these two steps in a systematic manner? For that, you need to break this chapter into various parts according to your wish. For instance, you can break the chapter into sections where each part will consist of 4 – 5 formulae and their applications. Study these parts accordingly.
When studying these sections you should read the theory part at least twice. Never go for cramming up the formulae. Always try to prove them by yourself and do this multiple times. Eventually you would not need to mug them up as you will remember them for a long time (revise them again and again to make yourself comfortable with them for the next two years).
Another method includes writing formulae again and again on a regular basis without actually proving them. This method can be mainly used in case we are not getting to the proof of any formula; for example sin(c+d) = sin(c)cos(d) + cos(c)sin(d). Its proof in S. L. Loney is actually a figure based proof which in turn is derived for a general triangle. Also, it can be cumbersome to always prove a sin(c) + sin(d) kind of formulae. So writing these again and again and solving questions which mainly include basic substitution of formula can to be helpful.
So far we’ve addressed memorizing formulae–but what about the questions in which you have to apply these formulae? For that you have to understand which formula you should use for a particular problem in order to save precious time. This makes your solution less crowded and mostly error-free.
The only solution to this problem is to practice more and more questions. I used to use M. L. Khanna as it contains a lot of questions to solve. This book contains questions of all levels ranging from a very basic level to a bunch of advanced level problems. Solutions are also provided.
You can also opt for some other book which provides you with questions. If you do not go to any coaching center or you don’t have a teacher who is on par with the JEE Advanced level, then a book with questions and their elaborate solutions will be very useful.
Finally, I would like to say that trigonometry is not a tough chapter and can be understood easily with some practice and revision. Since it is easier than other Mathematics chapters, it is more scoring too. Hence, practice the questions well to score good in JEE Maths. Good Luck!