Trigonometry is the mathematics of triangles and it is quite amazing that the understanding of the simple triangle leads to so many applications. The fundamental fact is that the angles of a triangle have a relationship to its sides, as well as to each other. As a result, you have the sine, cosine and other similar trigonometric functions.
The simplest application that we first learn about in school is how to measure the height of a tree or a building using the properties of a triangle. The same set of principles then applies to the study of astronomy and navigation, as much as to the fields of architecture and land-surveying.
A Class 12 student preparing for the board exams has no choice but to try and master trigonometry, as the questions from various streams such as relations and functions, algebra, calculus, vectors and 3D coordinate geometry could be based on trigonometry. About 20-25% of the questions in the board paper are likely to involve trigonometric terms, so do try and get on top of this subject.
Let us take a careful look at some of the maths streams requiring the use of trigonometry:
Relations and functions: Questions can be based on trigonometric functions as well as on inverse trigonometric functions.
Algebra: Some of the questions, especially the ones requiring proofs, are based on trigonometric ratios.
Calculus: In both differentiation and integration, a good number of questions are based on trigonometry.
Vectors and 3D coordinate geometry: Many of the basic terms and formulae of vectors and 3D geometry cannot be proved without using trigonometric ratios.
The following are some tips which will serve you well.
* Revise all of the trigonometric laws and identities, which were covered in Class 10 and 11, and make a chart for easy reference. You can also download free readymade charts from certain sites such as: http://www.ecalc.com/math-help)
* Revise the domain, range and graphs of all of the trigonometric and inverse trigonometric functions.
* Make sure you understand the difference between the trigonometric and inverse trigonometric functions.
Finally, practise, practise and practise. Try all the different types of questions that you can find on the subject, and check yourself as to where you are going wrong. When you catch yourself having made a mistake, recognise an opportunity for improvement. It may be a concept that you have not understood so far. Go back to your textbook and see if you have missed understanding something critical. If you cannot get the solution yourself, ask your friends or the teacher. Get to the bottom of that question, and once you have got it right, mark it out for future revision. You will invariably find that it’s the mistakes that you made during revision which led you to learn. Correcting those mistakes and learning from them will bring you those vital extra marks that you need.
The writer is founder & director, Second School Smart Tuitions