Trigonometry is one of the major topics in Maths subject. Trigonometry deals with the measurement of angles and sides of a triangle. Usually, trigonometry is considered for the right-angled triangle. Also, its functions are used to find out the length of the arc of a circle, which forms a section in the circle with a radius and its center point.
If we break the word trigonometry, ‘Tri’ is a Greek word which means ‘Three’, ‘Gon’ means ‘length’, and ‘metry’ means ‘measurement’. So basically, trigonometry is a study of triangles, which has angles and lengths on its side. Trigonometry basics consist of sine, cosine and tangent functions. Trigonometry for class 11 contains trigonometric functions, identities to solve complex problems more simply.
Table of Contents
Trigonometry Formulas
Here, you will learn trigonometry formulas for class 11 and trigonometric functions of Sum and Difference of two angles and trigonometric equations.
Starting with the basics of Trigonometry formulas, for a right-angled triangle ABC perpendicular at B, having an angle θ, opposite to perpendicular (AB), we can define trigonometric ratios as;
Sin θ = P/H
Cos θ = B/H
Tan θ = P/B
Cot θ = B/P
Sec θ = H/B
Cosec θ = H/P
Where,
P = Perpendicular
B = Base
H = Hypotenuse
Trigonometry Functions
Trigonometry functions are measured in terms of radian for a circle drawn in the XY plane. Radian is nothing but the measure of an angle, just like a degree. The difference between the degree and radian is;
Degree: If rotation from the initial side to the terminal side is (1/360)th of revolution, then the angle is said to measure 1 degree.
1 degree=60minutes
1 minute=60 second
Radian: If an angle is subtended at the center by an arc of length ‘l, the angle is measured as radian. Suppose θ is the angle formed at the center, then
θ = Length of the arc/radius of the circle.
θ = l/r
Relation between Degree and Radian:
2π radian = 360°
Or
π radian = 180°
Where π = 22/7
Learn more about the relation between degree and radian here.
Table for Degree and Radian relation
Degree
30°
45°
60°
90°
180°
270°
360°
Radian
π/6
π/4
π/3
π/2
π
3π/2
2π
Earlier we have discussed of trigonometric ratios for a degree, here we will write the table in terms of radians.
Trigonometry Table
Angle
0
π/6
π/4
π/3
π/2
π
3π/2
2π
sin θ
0
1/2
1/√2
√3/2
1
0
-1
0
cos θ
1
√3/2
1/√2
1/2
0
-1
0
1
tan θ
0
1/√3
1
√3
undefined
0
undefined
0
Sign of Trigonometric Functions
sin(-θ) = -sin θ
cos(-θ) = cos θ
tan(-θ) = -tan θ
cot(-θ) = -cot θ
sec(-θ) = sec θ
cosec(-θ) = -cosec θ
Click here to know more about the sign of trigonometric functions.
Also, go through the table given below to understand the behaviour of trigonometric functions with respect to their values in different quadrants.
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
sin
Increases from 0 to 1
Decreases from 1 to 0
Decreases from o to -1
Increases from -1 to 0
cos
Decreases from 1 to 0
Decreases from o to -1
Increases from -1 to 0
Increases from 0 to 1
tan
Increases from 0 to ∞
Increases from -∞ to 0
Increases from 0 to ∞
Increases from -∞ to 0
cosec
Decreases from ∞ to 1
Increases from 1 to ∞
Increases from -∞ to 1
Decreases from -1 to ∞
sec
Increases from 1 to ∞
Increases from -∞ to 1
Decreases from -1 to ∞
Decreases from ∞ to 1
cot
Decreases from ∞ to 0
Decreases from 0 to -∞
Decreases from ∞ to 0
Decreases from 0 to -∞
This behaviour can be observed from the trigonometry graphs.
Trigonometric Functions of Sum and Product of two angles
(I)
sin (x+y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y – cos x sin y
cos (x+y) = cos x cos y – sin x sin y
cos (x-y) = cos x cos y + sin x sin y
sin (π/2 – x) = cos x
cos (π/2 – x) = sin x
(II)
tan (x+y) = (tan x + tan y) /(1−tan x tan y)
tan (x-y) = (tan x − tan y)/(1 + tan x tan y)
cot (x+y) = (cot x cot y −1)/(cot y + cot x)
cot(x-y) = (cot x cot y + 1)/( cot y − cot x)
(III)
cos 2x = cos2 x-sin2 x = 2cos2 x-1 = 1-2sin2 x = (1-tan2 x)/(1+tan2 x)
sin 2x = 2sin x cos x= 2tan x/(1+ tan2 x)
tan 2x = 2 tan x/(1-tan2 x)
(IV)
sin 3x = 3 sin x – 4 sin3 x
cos 3x = 4 cos3 x – 3 cos x
tan 3x = [3tan x-tan3 x]/[1-3 tan2 x]
(V)
\(\begin{array}{l}cos\ x+ cos\ y=2\ cos{(\frac{x+y}{2})}\ cos{(\frac{x-y}{2})}\\ cos\ x – cos\ y = -2\ sin{(\frac{x+y}{2})}\ sin{(\frac{x-y}{2})}\\ sin\ x + sin\ y = 2\ sin{(\frac{x+y}{2})}\ cos{(\frac{x-y}{2})}\\ sin\ x – sin\ y = 2\ cos{(\frac{x+y}{2})}\ sin{(\frac{x-y}{2})}\end{array} \)
(VI)
2 cos x cos y = cos (x+y) + cos (x-y)
2 sin x sin y = cos (x-y) – cos (x+y)
2 sin x cos y= sin (x+y) + sin (x-y)
2 cos x sin y = sin (x+y) – sin (x-y)
To solve the trigonometric questions for class 11, all these functions and formulas are used accordingly. By practising those questions, you can memorize the formulas as well.
Solved Examples
Example 1:
Prove that sin(x+y)/ sin(x−y) = (tan x + tan y)/(tan x–tan y)
Solution:
We have
LHS = sin(x+y)/sin(x−y)
= (sin x cos y + cos x sin y)/(sin x cos y − cos x sin y)
Dividing numerator and denominator by cos x cos y, we get
= (tan x + tan y)/(tan x–tan y) ———–Proved.
Example 2:
Find the value of cos (31π/3).
Solution:
We know that the value of cos x repeats after the interval 2π.
Thus, cos (31π/3) = cos (10π + π/3)
= cos π/3 = 1/2
Trigonometric Functions and Their Properties
Sum and Product of Two Angles Formulas
Relation Between Degree and Radian in Trigonometry
Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations.
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CBSE Class 11 Maths Syllabus for 2023-24 with Marking Scheme
CBSE syllabus for class 11 Maths is divided into 5 units. The table below shows the units, number of periods and marks allocated for maths subject. The maths theory paper is of 80 marks and the internal assessment is of 20 marks.
No.
Units
Marks
I.
Sets and Functions
23
II.
Algebra
25
III.
Coordinate Geometry
12
IV.
Calculus
08
V.
Statistics and Probability
12
Total Theory
80
Internal Assessment
20
Grand Total
100
2025-26 CBSE Class 11 Maths Syllabus
Below you will find the CBSE Class Maths Syllabus for students.
Unit-I: Sets and Functions
1. Sets
Sets and their representations, empty sets, finite and infinite sets, equal sets, subsets, and subsets of a set of real numbers, especially intervals (with notations), universal set, Venn diagrams, union and intersection of sets, difference of sets, complement of a set and properties of complement.
2. Relations & Functions
Ordered pairs, Cartesian product of sets, number of elements in the Cartesian product of two finite sets, Cartesian product of the set of reals with itself (upto R x R x R), definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.
3. Trigonometric Functions
Positive and negative angles, measuring angles in radians and in degrees and conversion from one measure to another, definition of trigonometric functions with the help of unit circle, truth of the identity, signs of trigonometric functions, domain and range of trigonometric functions and their graphs, expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications.
Unit-II: Algebra
1. Complex Numbers and Quadratic Equations
Need for complex numbers, especially√−1, to be motivated by the inability to solve some of the quadratic equations. Algebraic properties of complex numbers, Argand plane.
2. Linear Inequalities
Linear inequalities, algebraic solutions of linear inequalities in one variable and their representation on the number line.
3. Permutations and Combinations
The fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of Formulae for nPr and nCr and their connections, simple applications.
4. Binomial Theorem
Historical perspective, statement and proof of the binomial theorem for positive integral indices, Pascal’s triangle, simple applications.
5. Sequence and Series
Sequence and series, arithmetic progression (A. P.), arithmetic mean (A.M.), geometric progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M.
Unit-III: Coordinate Geometry
1. Straight Lines
Brief recall of two-dimensional geometry from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Distance of a point from a line.
2. Conic Sections
Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.
3. Introduction to Three-Dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points.
Unit-IV: Calculus
1. Limits and Derivatives
Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit, limits of polynomials and rational functions trigonometric, exponential and logarithmic functions, definition of derivative relate it to the slope of the tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.
Unit-V: Statistics and Probability
1. Statistics
Measures of Dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped data.
2. Probability
Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.
Students can also get the syllabus of all the subjects by visiting CBSE Class 11 Syllabus page. Learn Maths & Science in an interactive & fun-loving way with Anand Classes App/Tablet.
Frequently Asked Questions on CBSE Class 11 Maths Syllabus 2025-26
Q1
What is the marks distribution for internals and theory exams according to the CBSE Maths Syllabus for Class 11?
The marks distribution for internals is 20 marks and the theory exam is 80 marks based on the CBSE Class 11 Maths Syllabus.
Q2
Which is the most important chapter in the CBSE Class 11 Maths Syllabus?
The important chapter in the CBSE Class 11 Maths Syllabus is Algebra which is for 25 marks in the overall weightage.
Q3
What are the chapters covered in Unit III of the CBSE Class 11 Maths Syllabus?
The chapters covered in Unit III of the CBSE Class 11 Maths Syllabus are straight lines, conic sections and an introduction to three-dimensional geometry.
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