Trigonometry is a branch of mathematics that deal with angles, lengths and heights of triangles and

relations between different parts of circles and other geometrical figures. Trigonometric Ratios and
identities are very useful and learning the below formulae help in solving the problems better.
Trigonometry formulas are essential for solving questions in Trigonometry Ratios and Identities in
Competitive Exams.
Trigonometric Ratio - relationship between the measurement of the angles and the length of the side
of the right triangle. These formulas relate lengths and areas of particular circles or triangles. On the
next page you’ll find identities. The identities don’t refer to particular geometric figures but hold for all
angles.

Trigonometry Formulas

Formulas for arcs and sectors of circles

You can easily find both the length of an arc and the area of a sector for an angle θ in a circle of
radius r.
Length of an arc. The length of the arc is just the radius r times the angle θ where the angle is
measured in radians. To convert from degrees to radians, multiply the number of degrees by π/180.
Arc = rθ.

Trigonometric Formulas - Right Angle

The most important formulas for trigonometry are those for a right triangle. If θ is one of the acute
angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse, the
cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite
side to the adjacent side

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Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of
a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in
familiar algebraic notation, (P)2 + (B)2 = (H)2
Applying Pythagoras theorem for the given right-angled theorem, we have:
(Perpendicular)2 + (Base)2 = (Hypotenuse)2
⇒ (P)2 + (B)2 = (H)2
The trigonometric properties are given below

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Reciprocal Relations

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Square Law Formulas

Along with the knowledge that the two acute angles are complementary, that is to say, they add to
90°, you can solve any right triangle:

● If you know two of the three sides, you can find the third side and both acute angles.
● If you know one acute angle and one of the three sides, you can find the other acute angle and
the other two sides.

Signs of Trigonometric Ratios

A lot of trigonometry formulas are based on the signs of trigonometric ratios, based on the quadrants
they lie in. Therefore it becomes extremely essential for us to understand how trigonometric ratios get
the positive or negative
sign. The sign is based on the quadrant in which the angle lies.

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Let us assume an angle of θ1 lying in the 1st quadrant and an angle θ in quadrant one and two
combined.
So let us see how signs change with respect to the quadrant they lie in.

● In Q1 all Trigonometric Ratios are positive. (Angles between 00 – 900)

● In Q2 all trigonometric ratios of sinθ and cosecθ are positive. (Angles between 900 – 1800)
● In Q3 all trigonometric ratios of cosθ and secθ are positive. (Angles between 1800 – 2700)
● In Q4 all trigonometric ratios of tanθ and cotθ are positive. (Angles between 2700 – 3600)

θ is the angle made between the x-axis and the line, in the anti-clockwise direction. If we move in the
clockwise direction, the angle will be taken as – θ. We know that in quadrant 4, only cosθ and secθ
will be positive, the others will be negative, therefore-

● Sin (– θ) = - Sin θ
● Cos (– θ) = Cos θ
● Tan (– θ) =- Tan θ
● Sec (– θ) = - Sec θ
● Cot (– θ) = - Cot θ

We need to understand that trigonometric ratios would change for angles- 90o ± θ and 270o ± θ and
they will remain same for 180o ± θ and 360o ± θ. Let’s see what happens when we add or subtract θ
from 90o ± θ and 270o ± θ

● Sec (90o + θ ) = Cos θ

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 ● Cot (90o - θ ) = Cos θ
● Tan (90o + θ ) = - Cot θ
● Tan (90o - θ ) = Cot θ
● Sec (90o + θ ) = Cosec θ
● Sec (90o + θ ) = Cosec θ
● Sin (270o - θ ) = - Cos θ
● Sin (270o - θ ) = - Cos θ

This is because any angle that is 2700+θ will fall in quadrant 4 and in this quadrant only trigonometric
ratios of cos
and sec are positive. So the above will be negative. 2700-θ will fall in the quadrant 3 and in this
quadrant trigonometric ratios of tan and cot are positive, so it will again be negative. For 180o ± θ and
for 360o ± θ, the signs will remain the same.

● Sin (360o + θ ) = Sin θ

● Sin (360o - θ ) = - Sin θ

For 3600+θ, the angle will complete one full rotation and then lie in quadrant 1 where all trigonometric
ratios are positive. So there are 2 important things to remember-

● The sign of the trigonometric ratios change based on the value of θ.

● sin becomes cos and cos becomes sin for 900+θ and for 2700+θ and it remains the same for
1800+θ
and for 3600+θ.

Trigonometry Formulas | Trigonometric Identities

After looking at the trigonometric ratios, let us move on to trigonometric identities, which are the
basics of most trigonometry formulas. The above identities hold true for any value of θ.

Trigonometry Formulas | Sum and Difference of Angles

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Trigonometry Formulas | Double Angle Formulas

Trigonometry Formulas | Triple Angle Formulas

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Trigonometry Formulas | Converting Product into Sum and Difference

Trigonometry Formulas | Values of Trigonometric Ratios

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Summary of Trigonometric Identities

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Periodicity and Periodic Identities

Half angle identities

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Complex relations

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Inverse trigonometric functions

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Complimentary angle

Negative arguments

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Reciprocal arguments

Values of Trigonometric Functions

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 CBSE Sample Papers for Class 10

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Solved CBSE Sample Papers for Class 10 Maths 2019

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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths solved by expert teachers and it is as an indispensable
tool for the students. We have taken utmost care while preparing Maths NCERT Solutions for
class 10 and the solutions are written in a proper form and as per the marking scheme
suggested by the CBSE.

NCERT Solutions for Class 10 Maths Chapter 1 Real

Numbers
● Real Numbers Class 10 Ex 1.1
● Real Numbers Class 10 Ex 1.2
● Real Numbers Class 10 Ex 1.3
● Real Numbers Class 10 Ex 1.4
● Extra Questions for Class 10 Maths Real Numbers

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

● Polynomials Class 10 Ex 2.1
● Polynomials Class 10 Ex 2.2
● Polynomials Class 10 Ex 2.3
● Polynomials Class 10 Ex 2.4
● Extra Questions for Class 10 Maths Polynomials

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NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear
Equations in Two Variables
● Pair Of Linear Equations In Two Variables Class 10 Ex 3.1
● Pair Of Linear Equations In Two Variables Class 10 Ex 3.2
● Pair Of Linear Equations In Two Variables Class 10 Ex 3.3
● Pair Of Linear Equations In Two Variables Class 10 Ex 3.4
● Pair Of Linear Equations In Two Variables Class 10 Ex 3.5
● Pair Of Linear Equations In Two Variables Class 10 Ex 3.6
● Pair Of Linear Equations In Two Variables Class 10 Ex 3.7
● Extra Questions for Class 10 Maths Linear Equations in Two Variables

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic

Equations
● Quadratic Equations Class 10 Ex 4.1
● Quadratic Equations Class 10 Ex 4.2
● Quadratic Equations Class 10 Ex 4.3
● Quadratic Equations Class 10 Ex 4.4
● Extra Questions for Class 10 Maths Quadratic Equations

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic

Progressions
● Arithmetic Progressions Class 10 Ex 5.1
● Arithmetic Progressions Class 10 Ex 5.2
● Arithmetic Progressions Class 10 Ex 5.3
● Arithmetic Progressions Class 10 Ex 5.4
● Extra Questions for Class 10 Maths Arithmetic Progressions

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NCERT Solutions for Class 10 Maths Chapter 6 Triangles
● Triangles Class 10 Ex 6.1
● Triangles Class 10 Ex 6.2
● Triangles Class 10 Ex 6.3
● Triangles Class 10 Ex 6.4
● Triangles Class 10 Ex 6.5
● Triangles Class 10 Ex 6.6
● Extra Questions for Class 10 Maths Triangles

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate

Geometry
● Coordinate Geometry Class 10 Ex 7.1
● Coordinate Geometry Class 10 Ex 7.2
● Coordinate Geometry Class 10 Ex 7.3
● Coordinate Geometry Class 10 Ex 7.4
● Extra Questions for Class 10 Maths Coordinate Geometry

NCERT Solutions for Class 10 Maths Chapter 8 Introduction

to Trigonometry
● Introduction to Trigonometry Class 10 Ex 8.1
● Introduction to Trigonometry Class 10 Ex 8.2
● Introduction to Trigonometry Class 10 Ex 8.3
● Introduction to Trigonometry Class 10 Ex 8.4
● Extra Questions for Class 10 Maths Introduction to Trigonometry

NCERT Solutions for Class 10 Maths Chapter 9 Some

Applications of Trigonometry
● Some Applications of Trigonometry Class 10 Ex 9.1
● Extra Questions for NCERT Class 10 Maths Applications of Trigonometry

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NCERT Solutions for Class 10 Maths Chapter 10 Circles
● Circles Class 10 Ex 10.1
● Circles Class 10 Ex 10.2
● Extra Questions for Class 10 Maths Circles

NCERT Solutions for Class 10 Maths Chapter 11

Constructions
● Constructions Class 10 Ex 11.1
● Constructions Class 10 Ex 11.2
● Extra Questions for Class 10 Maths Constructions

NCERT Solutions for Class 10 Maths Chapter 12 Areas

Related to Circles
● Areas Related to Circles Class 10 Ex 12.1
● Areas Related to Circles Class 10 Ex 12.2
● Areas Related to Circles Class 10 Ex 12.3
● Extra Questions for Class 10 Maths Areas Related to Circles

NCERT Solutions for Class 10 Maths Chapter 13 Surface

Areas and Volumes
● Surface Areas and Volumes Class 10 Ex 13.1
● Surface Areas and Volumes Class 10 Ex 13.2
● Surface Areas and Volumes Class 10 Ex 13.3
● Surface Areas and Volumes Class 10 Ex 13.4
● Surface Areas and Volumes Class 10 Ex 13.5
● Extra Questions for Class 10 Maths Surface Areas and Volumes

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NCERT Solutions for Class 10 Maths Chapter 14 Statistics
● Statistics Class 10 Ex 14.1
● Statistics Class 10 Ex 14.2
● Statistics Class 10 Ex 14.3
● Statistics Class 10 Ex 14.4
● Extra Questions for Class 10 Maths Statistics

Chapter 15 Probability
● Probability Class 10 Ex 15.1
● Probability Class 10 Ex 15.2
● Extra Questions for Class 10 Maths Probability

CBSE Class 10 Maths Unit-wise Weightage 2018-2019.

Scoring
UNIT No Name of the Unit Marks
1 Number Systems 6
2 Algebra 20
3 Coordinate Geometry 6
4 Geometry 15
5 Trigonometry 12
6 Mensuration 10
Statistics and
7 Probability 11
Total 80

Maths NCERT Solutions Class 10 Features:

● Strictly according to the latest CBSE guidelines.
● NCERT text book for Class 10 Exercises have been fully solved.
● It contains a large number of Extra Questions for CBSE Class 10 Maths.
● Each question has solved according to the CBSE marking scheme by our expert
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● NCERT Solutions for Class 10 Maths PDF
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● SAQs, VSAQs, Notes and many Resources for Circles
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● Video Solutions Surface Areas and Volumes
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