θ A B C Adjacent (cosθ) Opp. (sinθ) Hyp. sin²θ+cos²θ=1 1+tan²θ=sec²θ 1+cot²θ=cosec²θ sin(90−θ)=cosθ
sin θ
Chapter 8  ·  Class X Mathematics  ·  MCQ Practice

MCQ Practice Arena

Introduction to Trigonometry

Standard Angles, Identities and Ratios — Score Maximum in Minimum Time

📋 50 MCQs ⭐ 30 PYQs ⏱ 65 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
20Easy
20Medium
10Hard
30PYQs
65 secAvg Time/Q
7Topics
Easy 40% Medium 40% Hard 20%

Why Practise These MCQs?

CBSE Class XNTSEState BoardsOlympiad

Introduction to Trigonometry MCQs cover the six trig ratios, their standard angle values, Pythagorean identities, and complementary angle relations. CBSE Boards award 10–12 marks across Chapters 8 and 9. Identity-based proof MCQs are the highest-scoring topic here. NTSE includes standard angle substitution problems. Memorising the trig table for 0°, 30°, 45°, 60°, 90° alone covers 40% of MCQs.

Topic-wise MCQ Breakdown

Trigonometric Ratios (Definition)6 Q
Standard Angle Values (0°–90°)12 Q
Reciprocal & Quotient Relations6 Q
Pythagorean Identities10 Q
Complementary Angles (sin/cos, tan/cot)8 Q
Expression Simplification5 Q
Identity-Based Proofs (MCQ Form)3 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\sin^2\theta + \cos^2\theta = 1$
$1 + \tan^2\theta = \sec^2\theta$
$1 + \cot^2\theta = \text{cosec}^2\theta$
$\sin(90°-\theta)=\cos\theta,\ \tan(90°-\theta)=\cot\theta$
$\sin 30°=1/2,\ \sin 45°=1/\sqrt{2},\ \sin 60°=\sqrt{3}/2$

MCQ Solving Strategy

Memorise the full trig table (sin, cos, tan for 0°, 30°, 45°, 60°, 90°) — it covers nearly half the MCQs. For identity simplification, convert EVERYTHING to sin and cos first, then simplify. For complementary angle MCQs (sin(90°−θ)), just swap sin↔cos, tan↔cot, sec↔cosec. For Pythagorean identity MCQs, identify which of the three forms (sin²+cos²=1, sec²−tan²=1, cosec²−cot²=1) applies fastest.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Standard angle values, reciprocal relations, sin²+cos²=1

② Medium

Complementary angles, expression simplification with identities

③ Hard

Multi-identity proofs, find trig value given another, complex simplification

★ PYQ

CBSE — identity proof + value substitution; NTSE — angle reasoning

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Some Applications of Trigonometry
🎯 Knowledge Check

Maths — INTRODUCTION TO TRIGONOMETRY

50 Questions Class 10 MCQs
1
What is the value of \(\sin 30^\circ\)?
2
What is the value of \(\cos 60^\circ\)?
3
What is the value of \(\tan 45^\circ\)?
4
Which ratio equals \(\sin \theta\)?
5
Which ratio equals \(\cos \theta\)?
6
What is \(\tan 90^\circ\)?
7
What is the value of \(\sin 0^\circ\)?
8
What is \(\cos 0^\circ\)?
9
What is \(\tan 0^\circ\)?
10
What is \(\sec \theta\)?
11
What is \(\text{cosec }\theta\)?
12
What is \(\cot \theta\)?
13
The identity \(\sin^2\theta + \cos^2\theta = ?\)
14
\(1 + \tan^2\theta = ?\)
15
What is \(\sin 45^\circ\)?
16
What is \(\cos 90^\circ\)?
17
What is \(\tan 60^\circ\)?
18
What is \(\cot 45^\circ\)?
19
What is \(\sec 60^\circ\)?
20
What is \(\text{cosec }30^\circ\)?
21
\(\sin(90^\circ - \theta) = ?\)
22
\(\cos(90^\circ - \theta) = ?\)
23
\(\tan(90^\circ - \theta) = ?\)
24
If \(\sin \theta = \frac{3}{5}\), then \(\cos \theta = ?\)
25
If \(\cos \theta = \frac{12}{13}\), then \(\sin \theta = ?\)
26
If \(\tan \theta = \frac{3}{4}\), then \(\sec \theta = ?\)
27
Which equals \(\frac{\text{Hyp}}{\text{Adj}}\)?
28
What is \(\sin 90^\circ\)?
29
What is \(\tan 30^\circ\)?
30
If \(\sin \theta\) increases, \(\cos \theta\) ______.
31
Which ratio is always \(\le 1\)?
32
Which is always \(\ge 1\)?
33
If \(\sin \theta = \frac{4}{5}\), then \(\tan \theta = ?\)
34
If \(\tan \theta = 1\), then \(\theta = ?\)
35
Which side is opposite the right angle?
36
What is \(\cot 60^\circ\)?
37
What is \(\sec 0^\circ\)?
38
What is \(\text{cosec } 90^\circ\)?
39
If \(\text{Opp} = 7\), \(\text{Adj} = 24\), then \(\tan \theta = ?\)
40
If \(\cos \theta = \frac{4}{5}\), then \(\tan \theta = ?\)
41
What is \(\text{cosec }60^\circ\)?
42
For acute angles, which is always positive?
43
\(\sin \theta = \frac{\sqrt{3}}{2}\) for which angle?
44
\(\cos^2\theta = 1 - ?\)
45
If \(\cot \theta = \frac{5}{12}\), find \(\sin \theta\).
46
\(\sin 45^\circ \times \cos 45^\circ = ?\)
47
Trigonometric ratios depend on:
48
\(\tan \theta \cdot \cot \theta = ?\)
49
If \(\sin \theta = 1\), then \(\theta = ?\)
50
Which identity helps express \(\tan \theta\) in terms of \(\sin\theta, \cos\theta\)?
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🎓 Class 10 📐 Maths 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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Frequently Asked Questions

Trigonometry is the branch of mathematics that studies the relationship between the sides and angles of a right-angled triangle usin g trigonometric ratios such as sin e, cos in e, and tan gent.

Trigonometric ratios are ratios of the lengths of the sides of a right triangle with respect to one of its acute angles. They include sin , cos , tan , cos ec, sec , and cot .

The six ratios are: sin \(\theta\), cos \(\theta\), tan \(\theta\), cos ec\(\ \theta\), sec \(\theta\), and cot \(\theta\).

sin \(\theta\) = Opposite side ÷ Hypotenuse.

cos \(\theta\) = Adjacent side ÷ Hypotenuse.

tan \(\theta\) = Opposite side ÷ Adjacent side.

tan \(\theta\) = sin \(\theta\) ÷ cos \(\theta\).

cosec\(\ \theta\) = 1 ÷ sin \(\theta\) = Hypotenuse ÷ Opposite side.

sec \(\theta\) = 1 ÷ cos \(\theta\) = Hypotenuse ÷ Adjacent side.

cot \(\theta\) = 1 ÷ tan \(\theta\) = Adjacent side ÷ Opposite side.

Values include: sin 0\(^\circ\)=0, sin 30\(^\circ\)=1/2, sin 45\(^\circ\)=v2/2, sin 60\(^\circ\)=v3/2, sin 90\(^\circ\)=1 (others similarly defined).

They help solve real-life problems involving heights, distan ces, angles of elevation/depression, navigation, physics, engineering, and architecture.

The angle formed between the horizontal line and the line of sight when the observer looks upward at an object.

The angle formed between the horizontal line and the line of sight when the observer looks downward from a higher point.

sin ²\(\ \theta\) + cos ²\(\ \theta\) = 1.

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    INTRODUCTION TO TRIGONOMETRY – Learning Resources

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    📚
    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Some Applications Of Trigonometry | Mathematics Class -10
    Some Applications Of Trigonometry | Mathematics Class -10 — Complete Notes & Solutions · academia-aeternum.com
    🎓 Class -10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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