What should be my method to learn trigonometry?

Should I first learn the formulas and do a lot of formula based problems or should I start doing trigonometry problems straight away by looking at the formulas so that slowly I am able to learn them and have also done a lot of questions in meanwhile?

Actually I face this dilemma in almost every topic and subject.

Thanks!

Re: What should be my method to learn trigonometry?

Hey AaPa.

It really depends on what you want to learn.

Mathematics like any field of study has a lot of context. With mathematics you have all the formulae, proofs and identities but then in addition to this you have all the relations to real world problems which require a skill-set to translate words and pictures into mathematics.

Being able to solve things once you have all the formulas, constraints and equations/inequalities is one thing. Doing the word problems is another problem entirely.

Which things are you doing or want to do?

Re: What should be my method to learn trigonometry?

I want to be able to solve.

Re: What should be my method to learn trigonometry?

You should take a look at books like "How To Solve It" by the late George Polya. There is also a book called "How to Prove It" as well (by some other author whose name escapes me).

Basically to solve problems, you go through a few key steps.

1) Gather all the information that you canp

2) Set up some kind of model

3) Use the mathematical tools to arrive at a solution

4) Take that solution to try and explain the potential answer to that problem.

The first step requires you to take a problem and write down everything that has been given and everything that can be assumed. Sometimes the problem won't give you the assumptions: you have to do those yourself. It can take a bit of time before you are proficient to do this yourself, but when you are starting out - these will be given to you. You get the information from reading the problem, drawing pictures, looking at constraints, and writing down anything that is listed.

The second step requires you to take all the information and put it into mathematical form. The form consists of equations/inequalities, expressions, definitions, numerical values (variable and constant), and structural characteristics like integrals, matrices, vectors and so on.

The third step requires all the formulae, identities, and transformations that you learn as the mathematics itself. You basically take the stuff in step 2 and you keep changing your existing problem (which is hard) and turning it into a simpler problem. You keep doing this as long as you need to. You may need to either transform to another problem where all the information is constant, or you may not. An example could be that you approximate something which makes you lose information, but after doing that the problem has now become a lot easier to work with.

The final stage is taking your answer and explaining it in the context of the problem. If its a word problem or something physical, then you need to give meaning to what the numbers actually mean.

:Learning how to solve will take some practice in a variety of situations, but if you follow the above structures, read books like mentioned above, and practice problems in some form or another, then you will be able to solve more problems with more complexity as time goes on.

Re: What should be my method to learn trigonometry?