CBSE Class 10th Introduction to Trigonometry Details & Preparations Downloads
In the vast landscape of mathematics, there exists a powerful branch that holds the key to understanding the intricate relationships between angles and sides. Welcome to the world of trigonometry, where triangles become the building blocks for unraveling the mysteries of the universe. Trigonometry, derived from the Greek words "trigonon" (triangle) and "metron" (measure), serves as a mathematical toolkit essential for countless scientific and engineering applications.
Mastering Trigonometry A Comprehensive Guide with CBSE NCERT Download for a Solid Foundation
Trigonometric Ratios
Opposite & Adjacent Sides in a RightAngled Triangle
In the ΔABC rightangled at B, BC is the side opposite to ∠A, AC is the hypotenuse, and AB is the side adjacent to ∠A.
Trigonometric Ratios
For the right ΔABC, rightangled at ∠B, the trigonometric ratios of the ∠A are as follows:
 sin A=opposite side/hypotenuse=BC/AC
 cos A=adjacent side/hypotenuse=AB/AC
 tan A=opposite side/adjacent side=BC/AB
 cosec A=hypotenuse/opposite side=AC/BC
 sec A=hypotenuse/adjacent side=AC/AB
 cot A=adjacent side/opposite side=AB/BC
Relation between Trigonometric Ratios

cosec θ =1/sin θ

sec θ = 1/cos θ

tan θ = sin θ/cos θ

cot θ = cos θ/sin θ=1/tan θ
Visualization of Trigonometric Ratios Using a Unit Circle
Draw a circle of the unit radius with the origin as the center. Consider a line segment OP joining a point P on the circle to the center, which makes an angle θ with the xaxis. Draw a perpendicular from P to the xaxis to cut it at Q.

sin θ=PQ/OP=PQ/1=PQ

cos θ=OQ/OP=OQ/1=OQ

tan θ=PQ/OQ=sin θ/cos θ

cosec θ=OP/PQ=1/PQ

sec θ=OP/OQ=1/OQ

cot θ=OQ/PQ=cos θ/sin θ
Trigonometric Ratios of Specific Angles
The specific angles that are defined for trigonometric ratios are 0°, 30°, 45°, 60° and 90°.
Trigonometric Ratios of 45°
If one of the angles of a rightangled triangle is 45°, then another angle will also be equal to 45°.
Let us say ABC is a rightangled triangle at B, such that;
∠ A = ∠ C = 45°
Thus, BC = AB = a (say)
Using Pythagoras theorem, we have;
AC^{2} = AB^{2} + BC^{2}
= a^{2} + a^{2}
= 2a^{2}
AC = a√2
CBSE Class 10 NCERT Mathematics Topics for a Strong Foundation (NCERT DOWNLOAD)
Chapter Name  Introduction to Trigonometry 
Topic Number  Topics 
8.1  Introduction 
8.2  Trigonometric Ratios 
8.3  Trigonometric Ratios of Some Specific Angles 
8.4  Trigonometric Identities 
8.5  Summary 
Now, from the trigonometric ratios, we have
 sin 45° = (Opp. side to angle 45°)/Hypotenuse = BC/AC = a/a√2 = 1/√2
 cos 45° = (Adj. side to angle 45°)/Hypotenuse = AB/AC = a/a√2 = 1/√2
 tan 45° = BC/AB = a/a = 1
Similarly
 cosec 45° = 1/sin 45° = √2
 sec 45° = 1/cos 45° = √2
 cot 45° = 1/tan 45° = 1
The Historical Tapestry
Trigonometry's roots stretch far back in time, intertwining with the great civilizations of antiquity. Ancient astronomers, such as the Greeks and Indians, were among the first to recognize the significance of angles in the cosmos. From measuring the heights of towering pyramids to predicting celestial events, trigonometry became an indispensable tool for understanding the physical world.
The Language of Triangles
At its core, trigonometry revolves around the study of triangles. Whether you're dealing with rightangled triangles or more complex configurations, trigonometric functions like sine, cosine, and tangent emerge as the fundamental building blocks. These functions form the backbone of trigonometry, allowing us to relate the angles of a triangle to the lengths of its sides.
Range of Trigonometric Ratios from 0 to 90 Degrees
For 0∘≤θ≤90∘,

0 ≤ sin θ ≤ 1

0 ≤ cos θ ≤ 1

0 ≤ tan θ < ∞
1 ≤ sec θ < ∞ 
0 ≤ cot θ < ∞

1 ≤ cosec θ < ∞
tan θ and sec θ are not defined at 90∘.
cot θ and cosec θ are not defined at 0∘.
CBSE Class 10 Board Exam Sample Paper
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CBSE CLASS 10 Mathematics Chapters 
Chapter1: Real Numbers 
Chapter2: Polynomials 
Chapter3: Pair of Linear Equations in Two Variables 
Chapter4: Quadratic Equations 
Chapter5: Arithmetic Progressions 
Chapter6: Triangles 
Chapter7: Coordinate Geometry 
Chapter8: Introduction to Trigonometry 
Chapter9: Some Applications of Trigonometry 
Chapter10: Circles 
Chapter11: Areas Related to Circles 
Chapter12: Surface Areas and Volumes 
Chapter13: Statistics 
Chapter14: Probability 
CBSE CLASS 10 Science Chapters 
Chapter1: Chemical Reactions and Equations 
Chapter2: Acids, Bases and Salts 
Chapter3: Metals and Nonmetals 
Chapter4: Carbon and its Compounds 
Chapter5: Life Processes 
Chapter6: Control and Coordination 
Chapter7: How do Organisms Reproduce? 
Chapter8: Heredity 
Chapter9: Light – Reflection and Refraction 
Chapter10: The Human Eye and the Colourful World 
Chapter11: Electricity 
Chapter12: Magnetic Effects of Electric Current 
Chapter13: Our Environment 
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7. CBSE Class 10th Question Bank  View Page / Download 
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11. CBSE Class 10th Formula Booklet  View Page / Download 
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FAQ
Q1. What is Trigonometry?
Ans Trigonometry is a branch of mathematics that focuses on the relationships between the angles and sides of triangles. It explores the properties of these geometric elements and provides a set of functions to analyze and solve problems involving angles and distances.
Q2. Why is Trigonometry Important?
Ans Trigonometry is essential in various fields, such as physics, engineering, architecture, and astronomy. It helps in measuring distances, analyzing forces, designing structures, and understanding the behavior of waves and oscillations.
Q3. What are the Basic Trigonometric Functions?
Ans The fundamental trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions relate the angles of a triangle to the lengths of its sides and are crucial in solving trigonometric equations and applications.
Q4. How is Trigonometry Used in Real Life?
Ans Trigonometry has numerous realworld applications. It is used in navigation for calculating distances and directions, in physics to analyze waves and oscillations, and in architecture and engineering for designing structures and determining forces.
Q5. Can Trigonometry be Fun to Learn?
Ans Absolutely! Trigonometry might seem challenging at first, but many find it enjoyable once they grasp its concepts. Practical applications and handson problemsolving can make learning trigonometry a rewarding and engaging experience.