How to prepare trigonometry for NDA exam?

In this article, we will discuss some important tips and tricks to solve trigonometry questions quickly during the NDA exam.

Created On: Dec 11, 2018 15:37 IST
Modified On: Dec 11, 2018 18:19 IST
NDA preparation tips
NDA preparation tips

NDA exam is conducted by UPSC (Union Public Service Commission) twice in a year across the nation. After qualifying written exam & SSB interview, candidates are admitted to National Defence Academy, Khadakwasla, Maharashtra. NDA is considered to be the first tri-service academy in the world where cadets opted for the Air Force , Navy, and  Army are trained together for three years and then sent for further training at Air Force Academy, Indian Naval Academy, and Indian Military Academy to become a commissioned officer.

NDA exam is a very prominent exam among the young students, who have recently passed 12th class and aged below 19.5 years. The selection process is comprised of a written test followed by the SSB interview and the written test is conducted in the following two subjects-

  1. Mathematics (120 questions of 300 marks)
  2. General Ability Test (150 questions of 600 marks)

In Mathematics, trigonometry is one of the important chapters carrying second highest weightage after Algebra. The questions from trigonometry require rigorous practice and command on concepts to get high marks in this exam because these questions are not very general and straight-forward in nature.  To solve these questions, you must be aware of the right tricks so that maximum questions can be attempted in the given time frame.

In this article, we will discuss some important tips and tricks to solve trigonometry questions quickly during the NDA exam. Let us have a look on them-

NDA Exam preparation tips: Trigonometry

The topics under trigonometry cover angles & their measures (degrees, radians, etc.), trigonometric ratios, trigonometric identities, properties of triangle, trigonometric functions, applications of trigonometry, and etc. Before starting preparation, a candidate must be aware of the trigonometry syllabus. To prepare these topics, a candidate should follow the following tips & tricks-

Memorize the trigonometric ratios, values and identities

Trigonometry is very simple if you study it very well and in a systematic manner. Let us understand the basics of trigonometry one by one as described below-

i. Trigonometric Ratios- These ratios are the foundation of the trigonometry and you must understand them in a very conceptual way. There are 6 ratios in trigonometry namely- sin, cos, tan, cot, sec, and cosec. The method to find them in a right-angled triangle is as follow-




Perpendicular (L)

Base (A)

Perpendicular (L)

Hypotenuse (K)

Hypotenuse (K)

Base (A)




Now, some of you may be thinking, what this table is all about? Let us understand-

sin A = Perpendicular/ Hypotenuse;

cosec A= Hypotenuse/Perpendicular; (Here, A is the notation for representing an angle)

In the same way, you can interpret the other ratios as well.

ii. Trigonometric values- In the following table, we are giving you the values of these trigonometric ratios for some standard angles and their learning shortcuts as well-

These values are of high importance in trigonometry. We have also shared that method of getting these values in the above table. Please remember these values while attempting the questions.

iii. Trigonometric identities- Some important trigonometric identities relevant to the NDA exam are as follow-

The above figure implies that

a. All trigonometric ratios having angles less than 90 degrees have positive value.

For example - sin (90-A) = cos A; sec (90-A) =cosec A; and so on.

b. If 90o< A < 180o; then only sin and cosec remain positive.

For example- sin (90 + A) = cos A; sin (180 – A) = sin A;

cos(90 +A)=-sin A; sec (90 + A) = -cosec A;

c. If 180o< A < 270o; then only tan and cot remain positive.

For example- sin (180 +A) = -sinA; sin (270 –A)= -cos A;

cos (180 +A)=-cosA; cos (270 –A)= -sinA;

tan(180 + A) = tanA; tan (270 – A)=cotA;

d. If 270o< A < 360o; then only cos and sec remain positive.

Points to remember-

1. If angle is in the form of (90-A) or (270- A) or (90 +A) or (270 +A), then the ratio is altered with their complementary ratios. ‘sin’ is converted to ‘cos’, ‘cos’ is converted to ‘sin’, and so on.

sin (90-A) = cos A; cos (90 –A) = sin A;

tan (90-A)=cot A; cot (90-A)=tan A;

sec (90-A)=cosec A; cosec (90-A)= sec A;

2. If angle is in the form of (180-A)/(180+A) or (360 + A)/(360 – A); then the ratio is not going to change as illustrated below-

sin (180 –A)= sin A; sin (180 + A) = -sin A;

cos (180-A) =-cos A; cos (180 +A) = -cos A;

tan (180 –A) = -tan A; tan (180 + A) = tan A;

and so on for the further ratios as stated above in this point.

Apart from these concepts, we are sharing some important formulas, which will be helpful during solving the questions-



To prepare for the NDA exam, you are advised to refer only those books, which are relevant to the NDA syllabus. NDA exam is a very prestigious exam and every candidate want to qualify it at any cost. Therefore, candidates used to refer too many books to read the same topics or redundant topics. This is again a bad practice in which a lot of time and resources are wasted. Hence, we recommend you to refer only the standard books especially designed for NDA preparation. Few of them are given below-

  • Pathfinder for NDA & NA National Defence Academy Naval Academy Entrance Examination – Arihant Publications
  • Let's Crack NDA Exam - National Defence Academy & Naval Academy Examination-SSB Crack

Previous year papers

Previous year question papers also play an important role in cracking the NDA exam. Through solving these papers, you will get an idea about-

- The difficulty level of questions

- Types of questions

- Topic wise questions distribution

With the help of previous year question papers, you can set your priorities of studying a particular topic of the trigonometry chapter. Previous year question papers also give you an estimate of the efforts required to gain good marks in these questions as well. Hence, you should attempt these papers time to time and randomly so that you can testify your gained knowledge. There are numerous sources, where you can find the previous year papers. Few of them are given below-

  • 10 Practice Sets NDA & NA Entrance Exam – Arihant Publications
  • 12 Years NDA/NA Chapter-wise Solved Papers (2007-2018) 2018 – GK Publications
  • NDA KIT, A Book for NDA Entrance Exam Preparation 2018 Includes Previous 10 Years Papers with Web Support – Dhankar Publications

Time management

As we know that NDA exam is conducted in offline mode, you should be very vigilant while solving the question paper in exam. In offline exam, a candidate needs to read the question first and solve it on the rough paper. After solving the questions, he has to mark the answers on the OMR sheet. It is generally observed that candidates get too busy in solving the questions and they are not able to manage time in filling the answers in OMR sheet accordingly.  Sometimes, it became a reason of not making in NDA exam. Hence, we advise you to mark the answers in the OMR sheet periodically or you should allocate at least 10-15 minutes for marking the obtained answers in the last moment of the exam.


Practicing hard is the key to success in this exam. With practice, you can reduce the chance of getting wrong answers. It also increases your speed & concentration and builds your confidence for the exam. Hence, practice as much as you can, to qualify this exam with flying colors.

If you found the above information on “How to prepare Trigonometry for NDA exam?” useful, then visit our NDA|CDS webpage for more such information.

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