Chapter 3 of 18
Concept Maps
Ch 03 -Trigonometric Functions — Concept Maps
ICSE · Class 11 · Mathematics
4 concept maps of Ch 03 -Trigonometric Functions for ICSE Class 11 Mathematics, each also written out as a text outline.
103 questions36 flashcards15 formulas & key relations5 concepts
Interactive on Super Tutor
Studying Ch 03 -Trigonometric Functions? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for concept maps and more.
Free trial, no card needed.
Super Tutor
One of 10 illustrations for Ch 03 -Trigonometric Functions in Super Tutor — alongside flashcards, concept maps and practice questions.
4 Concept Maps
Complete Overview of Trigonometric Functions - Chapter 3
The map in words
- root((Trig Functions
- Class 11))
- Angle Measurement
- Degree System
- 1 degree = 1/360 revolution
- DMS Format
- 1 degree = 60 minutes
- 1 minute = 60 seconds
- Radian System
- SI Unit
- 180 degrees = pi
- Arc l = r theta
- Area = half r squared theta
- Degree System
- Six Trig Functions
- Basic Pair
- sin x = y coord
- cos x = x coord
- Derived Ratios
- tan = sin div cos
- cot = cos div sin
- sec = 1 div cos
- cosec = 1 div sin
- Domains and Ranges
- sin cos range -1 to 1
- tan cot range all reals
- sec cosec range beyond -1 and 1
- Basic Pair
- Identities
- Pythagorean
- sin sq + cos sq = 1
- sec sq - tan sq = 1
- cosec sq - cot sq = 1
- Allied Angles
- Negative angle
- pi by 2 plus minus x
- pi plus minus x
- 3pi by 2 plus minus x
- 2pi minus x
- Periodicity
- sin cos period 2pi
- tan cot period pi
- Pythagorean
- Addition Formulas
- sin A plus B
- cos A plus B
- tan A plus B
- cot A plus B
- Transformation
- Product to Sum
- 2 sinA cosB
- 2 cosA sinB
- 2 cosA cosB
- 2 sinA sinB
- Sum to Product
- sinC plus sinD
- sinC minus sinD
- cosC plus cosD
- cosC minus cosD
- Product to Sum
- Multiple Angles
- Double Angle
- sin 2x
- cos 2x four forms
- tan 2x
- Half Angle
- sin x by 2
- cos x by 2
- tan x by 2
- Triple Angle
- sin 3x
- cos 3x
- tan 3x
- Double Angle
- Special Values
- sin 18 = root5 minus 1 by 4
- cos 36 = root5 plus 1 by 4
- tan 22.5 = root2 minus 1
- Angle Measurement
Trigonometric Functions - Concept Map
The map in words
- Trigonometric Functions
- Angle Measurement
- Degrees
- DMS System
- Radians
- Arc Length = rθ
- Conversions
- Degree to Radian
- Radian to Degree
- Degrees
- Trigonometric Ratios
- Six Functions
- sin, cos, tan
- cot, sec, cosec
- Quadrants
- Q1: All positive
- Q2: sin, cosec positive
- Q3: tan, cot positive
- Q4: cos, sec positive
- Six Functions
- Trigonometric Identities
- Fundamental
- sin²x + cos²x = 1
- sec²x - tan²x = 1
- cosec²x - cot²x = 1
- Multiple Angles
- Double Angle
- sin 2x = 2sin x cos x
- cos 2x = cos²x - sin²x
- tan 2x = 2tan x/(1-tan²x)
- Triple Angle
- sin 3x = 3sin x - 4sin³x
- cos 3x = 4cos³x - 3cos x
- Double Angle
- Fundamental
- Transformations
- Sum to Product
- Product to Sum
- Sum and Difference
- A±B
- A±B
- A±B
- Applications
- Arc Length
- Sector Area
- Heights and Distances
- Periodic Phenomena
- Angle Measurement
Trigonometric Functions - Complete Concept Map
The map in words
- Trigonometric Functions
- Angle Measurement
- Degrees System
- 1 revolution = 360°
- 1° = 60 minutes
- 1 minute = 60 seconds
- Radian System
- 1 revolution = 2π rad
- Arc length l = rθ
- SI Unit
- Conversion
- 1° = π/180 rad
- 180° = π rad
- Degrees System
- Six Functions
- sin x
- Definition: y-coordinate
- Domain: all real numbers
- Range: [-1, 1]
- cos x
- Definition: x-coordinate
- Domain: all real numbers
- Range: [-1, 1]
- tan x
- Definition: sin x / cos x
- Domain: all except (2n+1)π/2
- Range: all real numbers
- cot x
- Definition: cos x / sin x
- Domain: all except nπ
- Range: all real numbers
- sec x
- Definition: 1 / cos x
- Domain: all except (2n+1)π/2
- Range: (-∞,-1] ∪ [1,∞)
- cosec x
- Definition: 1 / sin x
- Domain: all except nπ
- Range: (-∞,-1] ∪ [1,∞)
- sin x
- Identities
- Fundamental
- sin²x + cos²x = 1
- sec²x - tan²x = 1
- cosec²x - cot²x = 1
- Sum & Difference
- sin(A±B) formulas
- cos(A±B) formulas
- tan(A±B) formulas
- Double Angles
- sin 2x = 2 sin x cos x
- cos 2x = cos²x - sin²x
- tan 2x = 2tan x/(1-tan²x)
- Triple Angles
- sin 3x = 3sin x - 4sin³x
- cos 3x = 4cos³x - 3cos x
- tan 3x formula
- Half Angles
- sin(x/2) formulas
- cos(x/2) formulas
- tan(x/2) formulas
- Transformation
- Product to Sum
- Sum to Product
- Fundamental
- Allied Angles
- π/2 ± x
- sin(π/2-x) = cos x
- cos(π/2-x) = sin x
- π ± x
- sin(π-x) = sin x
- cos(π-x) = -cos x
- Other Angles
- Functions at π+x
- Functions at 3π/2±x
- Functions at 2π-x
- π/2 ± x
- Periodicity
- sin, cos, cosec, sec
- Period = 2π
- sin(x+2nπ) = sin x
- tan, cot
- Period = π
- tan(x+nπ) = tan x
- sin, cos, cosec, sec
- Sign Pattern
- Quadrant I
- All positive
- Quadrant II
- sin, cosec positive
- Quadrant III
- tan, cot positive
- Quadrant IV
- cos, sec positive
- Quadrant I
- Applications
- Heights and Distances
- Angle of elevation
- Angle of depression
- Circular Motion
- Arc length
- Sector area
- Periodic Phenomena
- Temperature cycles
- Sound waves
- Tides
- Engineering
- Design calculations
- Force analysis
- Heights and Distances
- Angle Measurement
Trigonometric Functions
The map in words
- Trigonometric Functions
- Angles and Measurement
- Unit Circle Definition
- Six Trigonometric Functions
- Signs in Quadrants
- Allied Angles
- Periodic Nature
- Trigonometric Identities
- Sum and Difference Formulas
Explore these maps interactively
Explore DiagramsFrequently Asked Questions
What are the important topics in Ch 03 -Trigonometric Functions for ICSE Class 11 Mathematics?
Key topics in Ch 03 -Trigonometric Functions include Angles, Degree, and Radian, Trigonometric Functions on the Unit Circle, Trigonometric Identities and Allied Angles, Sum, Difference, and Compound-Angle Formulas. Study these first, then practise questions on each for Class 11 exams.
What do the concept maps for Ch 03 -Trigonometric Functions show?
The 4 maps show how the ideas in Ch 03 -Trigonometric Functions connect: Complete Overview of Trigonometric Functions - Chapter 3; Trigonometric Functions - Concept Map. Each map is also written out as an outline on this page.
How should I revise Ch 03 -Trigonometric Functions for Class 11 exams?
Learn the core ideas first, then work through the 103 practice questions on Ch 03 -Trigonometric Functions. Revise definitions regularly and use flashcards for quick recall before the exam.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Ch 03 -Trigonometric Functions
Practice Quiz
Test yourself with a quick quiz
Important Questions
Exam-style questions with answers
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Study Plan
Step-by-step plan for this chapter
Flashcards
Quick-fire cards for active recall
Syllabus
What topics to cover
For serious students
Get the full Ch 03 -Trigonometric Functions chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for ICSE Class 11 Mathematics. Free to start, no card needed.