JEE Exam > JEE Notes > Mathematics (Maths) Main & Advanced > Revision Notes: Trigonometric Function
Revision Notes: Trigonometric Function
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Page 2 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Some Standard Results ? ta n ta n ta n(x + y) 1 ta n .ta n x y x y ? ? ? Page 3 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Some Standard Results ? ta n ta n ta n(x + y) 1 ta n .ta n x y x y ? ? ? cot(x +y) = cot x.cot y-1 coty + cotx ? sin (x - y) = sinx.cosy - cosx siny cos (x - y) = cosx cosy + sinxsiny ta n ta n ta n(x-y) 1 ta n .ta n x y x y ? ? ? cot .cot 1 cot(x-y) cot cot x y y x ? ? ? ? tan(x +y + z) = ta n ta n ta n ta n ta n ta n 1 ta n ta n ta n .ta n ta n ta n x y z x y z x y y z z x ? ? ? ? ? ? ? 2sinx cosy = sin(x + y) + sin(x - y) 2cosx siny = sin(x + y) - sin(x - y) 2cosx cosy = cos (x + y) + cos (x -y) 2sinx siny = cos (x + y) - cos (x + y) ? sin x + sin y = 2 sin x y ? cos x y ? cos x +cos y = 2 cos 2 x y ? cos 2 x y ? ? ? ? ? Page 4 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Some Standard Results ? ta n ta n ta n(x + y) 1 ta n .ta n x y x y ? ? ? cot(x +y) = cot x.cot y-1 coty + cotx ? sin (x - y) = sinx.cosy - cosx siny cos (x - y) = cosx cosy + sinxsiny ta n ta n ta n(x-y) 1 ta n .ta n x y x y ? ? ? cot .cot 1 cot(x-y) cot cot x y y x ? ? ? ? tan(x +y + z) = ta n ta n ta n ta n ta n ta n 1 ta n ta n ta n .ta n ta n ta n x y z x y z x y y z z x ? ? ? ? ? ? ? 2sinx cosy = sin(x + y) + sin(x - y) 2cosx siny = sin(x + y) - sin(x - y) 2cosx cosy = cos (x + y) + cos (x -y) 2sinx siny = cos (x + y) - cos (x + y) ? sin x + sin y = 2 sin x y ? cos x y ? cos x +cos y = 2 cos 2 x y ? cos 2 x y ? ? ? ? ? ? sin 2x = 2 sin x cos x = 2 2 tan 1 tan x x ? ? 2 2 1 ta n 1 ta n x x ? ? ? tan 2x = 2 2 tan 1 tan x x ? ? tan 3x = 3 2 3ta n ta n 1 3ta n x x x ? ? ? sin(x + y) sin(x — y) = sin x — sin y= cos y — cos x ? ? General solution — A solution of a trigonometric equation, generalised by means of periodicity, is known as the general solution. Principal solutions — The solutions of a trigonometric equation which lie in [0,2 ?) are called its principal solutions. ? sin ? = 0 ? ? ?? = n ? ? ? where ? n ? ? z ? cos ? = 0 ? ? ? ? = (2n ? ? ? 2 ? , where n ? ? z ? tan ? = 0 ? ? ?? = n ? ? ? where ? n ? ? z ? sin ? = sin ? ? ? ? ? = n ? ? ?(— 1) n ? ? where n ? z ? cos ? = cos ? ? ? ? ?? = 2n ? ? ? ? ? ? where n ? ? z ? tan ? = tan ? ? ? ? ?? = n ? ? ? ? ? ? where n ? ? z ? ? Page 5 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Some Standard Results ? ta n ta n ta n(x + y) 1 ta n .ta n x y x y ? ? ? cot(x +y) = cot x.cot y-1 coty + cotx ? sin (x - y) = sinx.cosy - cosx siny cos (x - y) = cosx cosy + sinxsiny ta n ta n ta n(x-y) 1 ta n .ta n x y x y ? ? ? cot .cot 1 cot(x-y) cot cot x y y x ? ? ? ? tan(x +y + z) = ta n ta n ta n ta n ta n ta n 1 ta n ta n ta n .ta n ta n ta n x y z x y z x y y z z x ? ? ? ? ? ? ? 2sinx cosy = sin(x + y) + sin(x - y) 2cosx siny = sin(x + y) - sin(x - y) 2cosx cosy = cos (x + y) + cos (x -y) 2sinx siny = cos (x + y) - cos (x + y) ? sin x + sin y = 2 sin x y ? cos x y ? cos x +cos y = 2 cos 2 x y ? cos 2 x y ? ? ? ? ? ? sin 2x = 2 sin x cos x = 2 2 tan 1 tan x x ? ? 2 2 1 ta n 1 ta n x x ? ? ? tan 2x = 2 2 tan 1 tan x x ? ? tan 3x = 3 2 3ta n ta n 1 3ta n x x x ? ? ? sin(x + y) sin(x — y) = sin x — sin y= cos y — cos x ? ? General solution — A solution of a trigonometric equation, generalised by means of periodicity, is known as the general solution. Principal solutions — The solutions of a trigonometric equation which lie in [0,2 ?) are called its principal solutions. ? sin ? = 0 ? ? ?? = n ? ? ? where ? n ? ? z ? cos ? = 0 ? ? ? ? = (2n ? ? ? 2 ? , where n ? ? z ? tan ? = 0 ? ? ?? = n ? ? ? where ? n ? ? z ? sin ? = sin ? ? ? ? ? = n ? ? ?(— 1) n ? ? where n ? z ? cos ? = cos ? ? ? ? ?? = 2n ? ? ? ? ? ? where n ? ? z ? tan ? = tan ? ? ? ? ?? = n ? ? ? ? ? ? where n ? ? z ? ? 5 1 sin18 4 ? ? ? ; 10 2 5 cos18 4 ? ? ? 10 2 5 5 1 sin36 ; cos36 4 4 ? ? ? ? ? ?Read More
FAQs on Revision Notes: Trigonometric Function
| 1. What are the key trigonometric ratios and how do they relate to a right triangle? |  |
Ans. The six main trigonometric ratios-sine, cosine, tangent, cotangent, secant, and cosecant-describe relationships between angles and sides in right triangles. Sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. These fundamental ratios form the foundation for solving angle and side problems in JEE Main & Advanced examinations. Students should memorise SOHCAHTOA as a quick recall method for primary trigonometric functions.
| 2. How do I remember all the trigonometric identities for JEE exams? | |
Ans. Trigonometric identities fall into key categories: reciprocal identities (like sin²θ + cos²θ = 1), quotient identities (tanθ = sinθ/cosθ), and co-function identities (sin(90°-θ) = cosθ). Rather than memorising each separately, understand that all derive from the Pythagorean identity. Refer to mind maps and flashcards that visually organise these relationships, making pattern recognition easier during high-pressure JEE problem-solving.
| 3. Why do trigonometric values repeat, and what's the period of sine and cosine? | |
Ans. Trigonometric functions are periodic because they describe rotational angles on the unit circle. Both sine and cosine repeat every 2π radians (360°), making their period 2π. Tangent repeats every π radians (180°) since it depends on the ratio of sine to cosine. Understanding periodicity helps solve trigonometric equations efficiently and predict function behaviour across multiple cycles on JEE question papers.
| 4. What's the difference between radians and degrees, and when should I use each? | |
Ans. Degrees divide a circle into 360 equal parts; radians measure angles using arc length relative to radius (2π radians = 360°). JEE Advanced typically uses radians for calculus-based problems and theoretical questions, while degrees appear in geometry and practical applications. Converting between them uses the formula: radians = degrees × (π/180). Mastering both units prevents calculation errors in mixed-format examination problems.
| 5. How can I quickly identify which trigonometric formula to apply when solving complex JEE problems? | |
Ans. Recognise problem patterns: sum-to-product formulas simplify additions like sinA + sinB, product-to-sum formulas handle products like sinA·sinB, and double-angle formulas (sin2θ = 2sinθcosθ) reduce higher multiples. Strategy involves examining the given expression's structure and matching it to a relevant trigonometric identity. Practising varied question types through worksheets and MCQ tests on EduRev builds pattern recognition speed essential for time-bound JEE Main examinations.
About this Document
10.6K Views
4.77/5 Rating
Apr 18, 2026 Last updated
Related Exams
Document Description: Revision Notes: Trigonometric Function for JEE 2026 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The notes and questions for Revision Notes: Trigonometric Function have been prepared according to the JEE exam syllabus. Information about Revision Notes: Trigonometric Function covers topics like and Revision Notes: Trigonometric Function Example, for JEE 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Revision Notes: Trigonometric Function.
Introduction of Revision Notes: Trigonometric Function in English is available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & Revision Notes: Trigonometric Function in Hindi for Mathematics (Maths) for JEE Main & Advanced course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Revision Notes: Trigonometric Function
Description
Revision Notes: Trigonometric Function of Maths with clear explanations of key concepts & important topics of the chapter, to help you underst& lessons better & revise quickly, & crack the JEE exam.
Information about Revision Notes: Trigonometric Function
In this doc you can find the meaning of Revision Notes: Trigonometric Function defined & explained in the simplest way possible. Besides explaining types of Revision Notes: Trigonometric Function theory, EduRev gives you an ample number of questions to practice Revision Notes: Trigonometric Function tests, examples and also practice JEE tests
Related Searches
Free, Sample Paper, Extra Questions, Objective type Questions, past year papers, Important questions, Revision Notes: Trigonometric Function, ppt, study material, Summary, Semester Notes, MCQs, Revision Notes: Trigonometric Function, Viva Questions, shortcuts and tricks, practice quizzes, Exam, Revision Notes: Trigonometric Function, Previous Year Questions with Solutions, mock tests for examination, video lectures, pdf ;