📐 CBSE · Class 10 · Mathematics · Chapter 8

Introduction to
Trigonometry

Complete chapter resources for CBSE Class 10 Maths — trig ratios, standard angle values, Pythagorean identities, sample questions, previous year board questions, and instant AI question paper generation.

4Topics
8–12Board marks
8Sample questions
3PYQ included
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Key Formulas — Chapter 8
  • sin A = Opposite / Hypotenuse
  • cos A = Adjacent / Hypotenuse
  • tan A = Opposite / Adjacent = sin A / cos A
  • Identity 1: sin²A + cos²A = 1
  • Identity 2: 1 + tan²A = sec²A
  • Identity 3: 1 + cot²A = cosec²A
Chapter Overview

What this chapter covers

Trigonometry is the study of relationships between the sides and angles of a right-angled triangle. Chapter 8 introduces the six trigonometric ratios — sine, cosine, tangent, cosecant, secant, and cotangent — defined with respect to an acute angle in a right triangle. Students learn to express each ratio in terms of the opposite side, adjacent side, and hypotenuse, and to find missing ratios when one ratio is given.

A central part of the chapter is the table of standard angle values for 0°, 30°, 45°, 60°, and 90°. These values are frequently substituted in both short-answer and long-answer board questions. The chapter also derives and requires students to apply the three Pythagorean identities: sin²A + cos²A = 1, 1 + tan²A = sec²A, and 1 + cot²A = cosec²A, which are the foundation for identity-proof questions worth 3–5 marks.

Board questions on this chapter span MCQs testing ratio identification, short-answer questions on complementary angles and identity simplification, and long-answer questions requiring multi-step proofs. Students who master the reciprocal relationships (cosec = 1/sin, sec = 1/cos, cot = 1/tan) and can manipulate the Pythagorean identities fluently are well-positioned to score full marks in this chapter.

Topics

What's inside Chapter 8

As per NCERT Class 10 Mathematics (CBSE syllabus)

Topic 1
Trigonometric Ratios
Definition of sin, cos, tan, cosec, sec, and cot for an acute angle A. Expressing each ratio as a fraction of the sides of a right-angled triangle and finding unknown ratios when one is given.
Topic 2
Trigonometric Ratios of Specific Angles
Exact values of all six ratios at 0°, 30°, 45°, 60°, and 90°. Derivations using equilateral and isosceles right triangles. Application in evaluating expressions involving standard angles.
Topic 3
Trigonometric Ratios of Complementary Angles
sin(90°−A) = cos A, tan(90°−A) = cot A, sec(90°−A) = cosec A, and their converses. Using these to simplify or evaluate expressions containing complementary angle pairs.
Topic 4
Trigonometric Identities
The three fundamental Pythagorean identities. Proving given identities by transforming one side into the other using algebraic manipulation and the basic ratio definitions.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Ch 6 · Triangles
Similar triangles, Pythagoras theorem — the geometric backbone of trig ratios
Class 9 · Number Systems & Algebra
Surds and radical simplification needed for standard angle values
Chapter 8 Introduction to
Trigonometry
Leads to
Ch 9 · Some Applications of Trigonometry
Heights and distances — direct application of trig ratios in real-world problems
Class 11 · Trigonometric Functions
Extension to all quadrants, general solutions, graphs, and inverse functions
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 10 board papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Objective 1 1–2 Standard angle value, ratio identification, or complementary angle result
Very Short Answer 2 1 Find missing ratio given one ratio, or evaluate an expression at a standard angle
Short Answer 3 1 Complementary angle simplification or a short identity proof
Long Answer / Identity Proof 4–5 1 Multi-step Pythagorean identity proof or case-based application question
Total (approximate) 8–12 4–5 Weightage varies across paper sets and years
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 10 Maths Chapter 8. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
The value of sin 30° + cos 60° is: (a) 0 (b) ½ (c) 1 (d) √3/2
Q2 Easy 2 marks Short Answer
If tan A = 4/3, find the value of sin A and cos A (where A is an acute angle).
Q3 Medium 2 marks Short Answer
Evaluate: (sin 35° / cos 55°) + (cos 12° / sin 78°) − 1
Q4 Medium 3 marks Short Answer
Without using trigonometric tables, evaluate: (sin 18° / cos 72°) + (√3 · tan 10° · tan 30° · tan 60° · tan 80°)
Q5 Medium 3 marks Short Answer
If sec A = 13/5, find all remaining trigonometric ratios of angle A.
Q6 Hard 4 marks Identity Proof
Prove that: (sin A + cosec A)² + (cos A + sec A)² = 7 + tan²A + cot²A
Q7 Hard 4 marks Identity Proof
Prove that: (tan A / (1 − cot A)) + (cot A / (1 − tan A)) = 1 + sec A · cosec A
Q8 Hard 5 marks Case-Based
A surveyor observes that from point P on the ground, the angle formed by the rope tied to the top of a vertical pole and the ground is 60°. The pole is 15√3 m tall. (i) Find the length of the rope (hypotenuse). (ii) Find the horizontal distance from point P to the base of the pole. (iii) If the surveyor moves 10 m closer to the pole, find the new value of tan of the angle the rope makes with the ground.
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 10 Maths board papers — Introduction to Trigonometry chapter.

Board 20222 marks
If sin A = 3/4, calculate cos A and tan A. (All India 2022)
Board 20233 marks
Prove that: (cosec A − sin A)(sec A − cos A) = 1 / (tan A + cot A). (Delhi 2023)
Board 20204 marks
Prove that: (sin θ − cos θ + 1) / (sin θ + cos θ − 1) = 1 / (sec θ − tan θ), using the identity sec²θ = 1 + tan²θ. (CBSE 2020)
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FAQ

Questions teachers ask

How many marks does Introduction to Trigonometry carry in the CBSE Class 10 board exam? +
Typically 8–12 marks across 4–5 questions — one or two 1-mark MCQs, a 2-mark short answer on identities or standard angles, and one 4–5 mark long-answer or case-based question. The chapter has appeared in every CBSE Class 10 Maths board paper for the past decade and is one of the highest-weightage chapters in the Geometry & Trigonometry unit.
What are the six trigonometric ratios and how are they defined in a right-angled triangle? +
For an acute angle A in a right-angled triangle: sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent. The reciprocals give cosec A = 1/sin A, sec A = 1/cos A, and cot A = 1/tan A. CBSE board questions frequently test whether students can identify the correct sides and apply the right ratio without mixing them up.
Which trigonometric identities are most important for the CBSE Class 10 board exam? +
The three Pythagorean identities are essential: (1) sin²A + cos²A = 1, (2) 1 + tan²A = sec²A, and (3) 1 + cot²A = cosec²A. Board questions based on these identities — especially proving that an expression equals 1 or simplifying a given expression — appear in almost every year's paper and are typically worth 3–5 marks.
Do students need to memorise the standard angle table for the board exam? +
Yes. The values of sin, cos, tan, cosec, sec, and cot for 0°, 30°, 45°, 60°, and 90° must be memorised. A quick memory trick: for sin, write √0, √1, √2, √3, √4 for the five angles and divide each by 2. Cos is the reverse order of sin. Tan = sin/cos. Board MCQ and short-answer questions routinely substitute these values directly.
How do I generate a custom question paper for Introduction to Trigonometry using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 10 Mathematics, select Chapter 8 (Introduction to Trigonometry), set your preferred question-type mix (MCQ, short answer, identity proof, word problem) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.