Trigonometry is the concept that most students fear when preparing for the JEE exam. The teachers and experts motivate their students to grasp the basics of this topic. Trigonometry is an extremely important concept of mathematics with many different concepts and formulas. The applications of Trigonometry are everywhere in this world. Trigonometry is used to determine the distance of an airplane flying from the human eye using simple formulas. It can also be applied to find the speed of moving objects. For JEE 2022 aspirants Trigonometry is a very crucial topic. Trigonometry has a wide application in engineering. Topics like analog signal designing and satellite communication include a lot of derivations that are solved using advanced Trigonometry.
In this article, a student will learn about all the necessary information related to Trigonometry. From the fundamental concepts to advanced derivations, this article will make a student confident enough to solve any problem that appears in JEE Mains exam or JEE Advanced exam related to Trigonometry. At least 2-3 questions will appear on this topic. A student will be able to solve all the questions in JEE 2022 after going through this article. So without further ado, let us begin.
|Table of Contents|
|Basic Trigonometric Identities|
|Value of Trigonometric Ratios at Standard Angles|
|Trigonometric Identities of Compound Angles|
|Trigonometric Identities of Multiple Angles|
The term trigonometry comes from the Greek word, meaning measurement. To be precise, measurement of the right-angled triangles. The various trigonometric ratios can be derived from the sides of the right-angled triangle. Utilising their length and angles, multiple trigonometric ratios can be formed. The basic forms of trigonometric ratios are:
Let us learn about the trigonometric ratios one at a time:
Basic Trigonometric Ratios
Sine: The sine function is the basic trigonometric function, abbreviated as sin. It is the ratio of the size of the perpendicular of a right-angle triangle to its hypotenuse. Mathematically,sin (k) = altitude (perpendicular) /hypotenuse or p/h, where ‘k’ is the angle between the two sides.
Cosine: Cosine is another basic trigonometric function, other than sine. Sine and cosine are the fundamentals that derive other trigonometric functions, like tangent, cosecant, secant, and cotangent. Cosine is abbreviated as cos, and is the ratio of the length of the base of a right-angle triangle to its hypotenuse. cos (x) = base of the triangle divided to its hypotenuse, where ‘x’ is the angle between the two sides.
Tangent: Tangent is derived from the basic trigonometric functions, cosine and sine. It is the ratio of sine to cosine, and expressed as the ratio between the perpendicular of a right-angled triangle to its base. It is abbreviated as ‘tan’ and can be expressed as p/h. Mathematically, it is represented by,
Tan (p) = sin (p) / cos (p).
These trigonometric functions, sine, cosine and tangent, form the basic trigonometric ratios. The other ratios are made by inverting these ratios.
Derived Trigonometric Ratios
Cosecant: Cosecant is the multiplicative inverse of the first trigonometric ratio, i.e., sine. It is abbreviated as ‘cosec’, and can be referred to as the ratio of the hypotenuse to the perpendicular. Cosec (k) = 1/sin (k) or h/p.
Secant: The trigonometric ratio secant is the multiplicative inverse of the second trigonometric ratio, i.e., cosine. It is abbreviated as ‘secant’ and defined as the ratio of the hypotenuse of a right-angle triangle to the base of the same triangle. Sec (k) = 1/cos (k) or h/b.
Cotangent: Cosecant is the multiplicative inverse of the third trigonometric ratio, i.e., tan. A cot is expressed as the ratio of the base of a right-angle triangle to its perpendicular. Also, cotegant can be defined as the ratio of the cos function of a triangle to its sin function. Cot (k) = 1/tan (k), or b/p, or cos (k) / sin (k).
Basic Trigonometric Identities
A student must have the below mentioned trigonometric identities learnt by heart. They are not asked directly in JEE 2022 and other olympiads but can be indirectly asked in complex questions. To prevent mistakes, a student must have these formulas on the tip of their fingers. All the other identities are derived from these basic ones. The identities are:
- sin2(a) + cos2(a) = 1
- 1 + cot2(a) = cosec2(a)
- 1 + tan2(a) = sec2(a)
- sec (a) – tan (a) = 1sec(a) + tan(a)
- cosec (a) – cot (a) = 1cosec(a) + cot(a)
- sin4(a) + cos2(a) = 1 – 2 cos2(a)sin2(a)
Value of Trigonometric Ratios at Standard Angles
The table mentioned below is an important asset for learning Trigonometry. A student can find the value of any standard trigonometric function if they have this table imprinted in their minds. The table below is also beneficial for Physics and Chemistry questions. Students must make sure to follow this table accurately.
This completes the basic information related to Trigonometry, which can arrive in JEE Advanced 2022 and other competitive exams in India like CUCET and KVPY. From the next topic, concepts will be complex but not hard. So let us see the complex Maths concepts related to Trigonometry.
Trigonometric Identities of Compound Angles
Assume that we have an angle that is the sum or difference of the other two angles. The values of the two angles are unknown. How will you calculate the value of the trigonometric ratio in such cases? The answer is simple: A student must learn the below-mentioned identities for compound angles, and they can easily solve any question. The standard trigonometric identities are:
- sin (K ± L) = sin K cos L ± cos K sin L
- cos (K ± L) = cos K cos L ∓ sin K sin L
- tan (K+L) = tan K ± tan L1 ± tan K.tan L
- cot (K+L) = cot K.cot LF ∓ 1cot L±cot K
- sin (K + L) sin (K – L) = sin2K – sin2L = cos2L – cos2K
- cos (K + L) cos (K – L) = cos2K – sin2L = cos2L – sin2K
- sin (K+L+M) = sin K cos L cos M + sin L cos K cos M + sin M cos K cos L – sin K sin L sin M
- cos (K+L+M) = cos K cos L cos M – cos K sin L sin M – cos L sin K sin M – cos M sin K sin L
- tan (K+L+ M) = tan K+tan L+tan M-tan Ktan Ltan M1 – tan K.tan L – tan L.tan M – tanM.tan K
Trigonometric Identities of Multiple Angles
When a student finds questions having the angle multiplied by some parameter they can use the following formulas:
- sin 2K = 2 sinK cosK= 2 tan K/1+tan2K
- cos 2K = 2cos2K – 1=1 – 2sin2K = 1-tan2K/1+tan2K = cos2K – sin2K
- tan 2K = 2tanK/1-tan2K
- sin3K = 3 sin K – 4sin3K
- cos 3K = 4cos3K – 3 cos K
- tan 3K = 3tan K-tan3K/1-3tan2K
- 2 sin K cos L = sin (K+L) + sin (K – L)
- 2 sin L cos K = sin (K + L) – sin (K – L)
- 2 cos K cos L=cos (K + L) + cos (K – L)
- 2 sin K sin L = cos (K – L) – cos (K + L)
- sin M+sin N=2 sin (M+N2) cos (M-N2)
- sin M – sin N= 2 cos (M+N2) sin(M-N2)
- cos M – cos N= 2 cos (M+N2) cos (M-N2)
- cos M – cos N=2 sin (M+N2) sin (N-M2)
In the following solutions of trigonometric equations, n belongs to Z (Integers).
|sin (a) = 0||nπ|
|cos (a) = 0||(2n+1)π2|
|tan (a) = 0||nπ|
|sin (a) = sin (b)||nπ + (-1)n.b|
|cos (a) = cos (b)||2nπ ± b|
|tan (a) = tan (b)||nπ + b|
This concludes all the basic trigonometric concepts for JEE aspirants. All the advanced concepts begin when a student has fully grasped these fundamental concepts. At first glance, the topics can be pretty irritating and hard to understand. We advise the students not to panic and go line by line through the notes mentioned above. Students can seek solutions to their problems in NCERT solutions. Everyone is not perfect, some students may complete this article in one day, and some may take one week. The above notes are written in easy-to-understand language so that everyone who visits this article fully grasps the Maths concepts written on it.
1. What is the best way to prepare for JEE Main 2022 Trigonometry?
It is critical to have two things when studying for the JEE Trigonometry unit of the maths syllabus: the correct study schedule and the right study tools. We recommend the students start studying a few months before the exam, so they have enough time to absorb everything. A student should also go over their textbooks and answer any practice questions listed in each chapter. Finally, a few days before the exam, go over the JEE Trigonometry concept notes on this page to rapidly go over what you’ve learned in this course.
2. Is it possible to get the JEE Trigonometry concept notes for free?
Yes! JEE aspirants can access Trigonometry concept notes on Aakash’s website. A student may download the JEE Trigonometry Revision Notes for free. If a student has an Aakash account, they can download these notes as a PDF file. Creating an account on Aakash’s is simple. Sign up for free using your phone number or email address. Once a student has registered an account, they will have quick access to the website’s thousands of resources. Furthermore, all of Aakash’s resources like NCERT Solutions for Class 12 Maths and NCERT Solutions for Class 11 Maths are generated by experts. As a result, these are some of the highest-quality study materials available worldwide.
3. What are the benefits of downloading JEE Main 2022 Trigonometry concept notes?
Concept notes are especially handy in the days leading up to an exam when you need to review a unit but don’t have time to read over your textbooks, reference books, or notes. They allow students to rapidly skim over the chapter while simultaneously learning everything they need to know for the exam. Maths professionals also produced these revision notes, so skimming through them is nearly the same as receiving a Maths expert lesson.
4. What will be covered in the JEE Main 2022 Trigonometry concept notes?
The JEE Main 2022 Trigonometry concept notes cover all of the important chapters in the Trigonometry unit of the JEE Main Maths syllabus. The topics covered include a lot of trigonometric identities and equations, general solutions of trigonometric functions, and inverse trigonometric functions. The concept notes of Trigonometry explain the concepts in a straightforward way to better aid students who may be struggling with this chapter.
5. Where can I get more study materials for JEE basic Trigonometry?
Aakash’s website contains all you’ll need to prepare for the JEE Maths Syllabus’s Trigonometry unit. The syllabus, mock tests, previous year papers, significant questions, and other information are available. The website also provides reference books solutions like RD Sharma solutions and RS Aggarwal solutions in the common person’s language. On the website, you may get all of these resources for free. This page offers a PDF copy of Trigonometry revision notes. You can also get the important questions on the website that may appear in JEE 2022 and the national engineering olympiad. If possible, find Aakash Coaching Institute near you for studies.