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

⚠tan 90° is UNDEFINED — students often write it as 0 or ∞ incorrectly
⚠sin 0° = 0, cos 0° = 1 — confuse these and lose easy marks
⚠Complementary: sin(90°−θ) = cosθ, NOT sinθ
⚠sec²θ − tan²θ = 1 (not sin²+cos²=1) — use the right identity
⚠cosec θ = 1/sinθ, NOT 1/cosθ

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

What is the value of $\sin 30^\circ$?

a a. 1 b b. $\frac{1}{2}$ c c. $\frac{\sqrt{3}}{2}$ d d. 0

What is the value of $\cos 60^\circ$?

a a. 1 b b. $\frac{1}{2}$ c c. $\frac{\sqrt{3}}{2}$ d d. 0

What is the value of $\tan 45^\circ$?

a a. 0 b b. 1 c c. $\sqrt{3}$ d d. $\frac{1}{\sqrt{3}}$

Which ratio equals $\sin \theta$?

a a. $\frac{\text{Opp}}{\text{Hyp}}$ b b. $\frac{\text{Adj}}{\text{Hyp}}$ c c. $\frac{\text{Opp}}{\text{Adj}}$ d d. $\frac{\text{Hyp}}{\text{Opp}}$

Which ratio equals $\cos \theta$?

a a. $\frac{\text{Opp}}{\text{Hyp}}$ b b. $\frac{\text{Adj}}{\text{Hyp}}$ c c. $\frac{\text{Opp}}{\text{Adj}}$ d d. $\frac{\text{Hyp}}{\text{Opp}}$

What is $\tan 90^\circ$?

a a. 0 b b. 1 c c. Undefined d d. $\infty$

What is the value of $\sin 0^\circ$?

a a. 0 b b. 1 c c. $\frac{1}{2}$ d d. $\frac{\sqrt{3}}{2}$

What is $\cos 0^\circ$?

a a. 1 b b. 0 c c. $\frac{\sqrt{2}}{2}$ d d. $\frac{1}{2}$

What is $\tan 0^\circ$?

a a. 1 b b. 0 c c. Undefined d d. $\sqrt{3}$

What is $\sec \theta$?

a a. $\frac{1}{\tan \theta}$ b b. $\frac{1}{\cos \theta}$ c c. $\frac{1}{\sin \theta}$ d d. $\frac{1}{\cot \theta}$

What is $\text{cosec }\theta$?

a a. $\frac{1}{\sin \theta}$ b b. $\frac{1}{\cos \theta}$ c c. $\frac{1}{\tan \theta}$ d d. $\frac{1}{\cot \theta}$

What is $\cot \theta$?

a a. $\frac{1}{\tan \theta}$ b b. $\frac{\sin \theta}{\cos \theta}$ c c. $\frac{1}{\sin \theta}$ d d. $\frac{\cos \theta}{\sin \theta}$

The identity $\sin^2\theta + \cos^2\theta = ?$

a a. $\sin \theta$ b b. $\cos \theta$ c c. 1 d d. $\sec \theta$

$1 + \tan^2\theta = ?$

a a. $\cos^2\theta$ b b. $\sec^2\theta$ c c. $\text{cosec}^2\ \theta$ d d. $\sin^2\theta$

What is $\sin 45^\circ$?

a a. $\frac{1}{2}$ b b. $\frac{\sqrt{3}}{2}$ c c. $\frac{\sqrt{2}}{2}$ d d. 1

What is $\cos 90^\circ$?

a a. 1 b b. 0 c c. $-1$ d d. $\frac{\sqrt{2}}{2}$

What is $\tan 60^\circ$?

a a. 1 b b. $\sqrt{3}$ c c. $\frac{1}{\sqrt{3}}$ d d. 0

What is $\cot 45^\circ$?

a a. 1 b b. 0 c c. $\sqrt{3}$ d d. $\frac{1}{\sqrt{3}}$

What is $\sec 60^\circ$?

a a. 2 b b. $\frac{1}{2}$ c c. $\sqrt{3}$ d d. $\frac{2}{\sqrt{3}}$

What is $\text{cosec }30^\circ$?

a a. 1 b b. 2 c c. $\sqrt{3}$ d d. $\frac{1}{2}$

$\sin(90^\circ - \theta) = ?$

a a. $\cos \theta$ b b. $\sin \theta$ c c. $\tan \theta$ d d. $\cot \theta$

$\cos(90^\circ - \theta) = ?$

a a. $\sin \theta$ b b. $\tan \theta$ c c. $\cot \theta$ d d. $\sec \theta$

$\tan(90^\circ - \theta) = ?$

a a. $\sec \theta$ b b. $\cot \theta$ c c. $\tan \theta$ d d. $\cos \theta$

If $\sin \theta = \frac{3}{5}$, then $\cos \theta = ?$

a a. $\frac{3}{5}$ b b. $\frac{4}{5}$ c c. $\frac{\sqrt{5}}{3}$ d d. $\frac{5}{3}$

If $\cos \theta = \frac{12}{13}$, then $\sin \theta = ?$

a a. $\frac{12}{13}$ b b. $\frac{5}{13}$ c c. $\frac{13}{12}$ d d. $\frac{1}{13}$

If $\tan \theta = \frac{3}{4}$, then $\sec \theta = ?$

a a. $\frac{5}{4}$ b b. $\frac{5}{3}$ c c. $\frac{4}{5}$ d d. $\frac{3}{5}$

Which equals $\frac{\text{Hyp}}{\text{Adj}}$?

a a. $\sin \theta$ b b. $\sec \theta$ c c. $\cot \theta$ d d. $\text{cosec }\theta$

What is $\sin 90^\circ$?

a a. 0 b b. 1 c c. $\frac{\sqrt{3}}{2}$ d d. $\frac{1}{2}$

What is $\tan 30^\circ$?

a a. 1 b b. $\frac{1}{\sqrt{3}}$ c c. $\sqrt{3}$ d d. $\frac{1}{2}$

If $\sin \theta$ increases, $\cos \theta$ ______.

a a. increases b b. decreases c c. stays constant d d. becomes undefined

Which ratio is always $\le 1$?

a a. $\sin \theta$ b b. $\cos \theta$ c c. Both a & b d d. $\tan \theta$

Which is always $\ge 1$?

a a. $\sin \theta$ b b. $\cos \theta$ c c. $\sec \theta$ d d. $\tan \theta$

If $\sin \theta = \frac{4}{5}$, then $\tan \theta = ?$

a a. $\frac{3}{4}$ b b. $\frac{4}{3}$ c c. $\frac{5}{4}$ d d. $\frac{1}{3}$

If $\tan \theta = 1$, then $\theta = ?$

a a. $0^\circ$ b b. $30^\circ$ c c. $45^\circ$ d d. $90^\circ$

Which side is opposite the right angle?

a a. Opposite side b b. Adjacent side c c. Hypotenuse d d. None

What is $\cot 60^\circ$?

a a. $\frac{1}{\sqrt{3}}$ b b. $\sqrt{3}$ c c. 1 d d. 0

What is $\sec 0^\circ$?

a a. 0 b b. 1 c c. Undefined d d. 2

What is $\text{cosec } 90^\circ$?

a a. 0 b b. 1 c c. Undefined d d. 2

If $\text{Opp} = 7$, $\text{Adj} = 24$, then $\tan \theta = ?$

a a. $\frac{7}{24}$ b b. $\frac{24}{7}$ c c. $\sqrt{7^2+24^2}$ d d. $\frac{1}{24}$

If $\cos \theta = \frac{4}{5}$, then $\tan \theta = ?$

a a. $\frac{3}{4}$ b b. $\frac{4}{3}$ c c. $\frac{5}{3}$ d d. $\frac{3}{5}$

What is $\text{cosec }60^\circ$?

a a. $\frac{2}{\sqrt{3}}$ b b. $\sqrt{3}$ c c. 1 d d. 2

For acute angles, which is always positive?

a a. $\sin \theta$ b b. $\cos \theta$ c c. $\tan \theta$ d d. All of these

$\sin \theta = \frac{\sqrt{3}}{2}$ for which angle?

a a. $30^\circ$ b b. $45^\circ$ c c. $60^\circ$ d d. $90^\circ$

$\cos^2\theta = 1 - ?$

a a. $\sin^2\theta$ b b. $\cot^2\theta$ c c. $\tan^2\theta$ d d. $\sec^2\theta$

If $\cot \theta = \frac{5}{12}$, find $\sin \theta$.

a a. $\frac{5}{13}$ b b. $\frac{12}{13}$ c c. $\frac{13}{12}$ d d. $\frac{1}{13}$

$\sin 45^\circ \times \cos 45^\circ = ?$

a a. $\frac{1}{2}$ b b. $\frac{1}{\sqrt{2}}$ c c. $\frac{1}{\sqrt{3}}$ d d. $\frac{\sqrt{3}}{2}$

Trigonometric ratios depend on:

a a. size of triangle b b. angle of triangle c c. perimeter d d. area

$\tan \theta \cdot \cot \theta = ?$

a a. 1 b b. 0 c c. $\sin \theta$ d d. $\cos \theta$

If $\sin \theta = 1$, then $\theta = ?$

a a. $0^\circ$ b b. $30^\circ$ c c. $90^\circ$ d d. $45^\circ$

Which identity helps express $\tan \theta$ in terms of $\sin\theta, \cos\theta$?

a a. $\sin^2\theta + \cos^2\theta = 1$ b b. $\tan \theta = \frac{\sin \theta}{\cos \theta}$ c c. $1 + \tan^2\theta = \sec^2\theta$ d d. $\sin(90^\circ - \theta) = \cos \theta$

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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.

INTRODUCTION TO TRIGONOMETRY – Learning Resources

Detailed Notes

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NCERT Solutions

ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025

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Introduction to Trigonometry

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — INTRODUCTION TO TRIGONOMETRY

Frequently Asked Questions

Q 01 What is trigonometry in simple terms?

Q 02 What is the meaning of trigonometric ratios?

Q 03 What are the six trigonometric ratios for an acute angle?

Q 04 How is sin \(\theta\) defined in a right-angled triangle?

Q 05 How is cos \(\theta\) defined?

Q 06 How is tan \(\theta\) defined?

Q 07 What is the relationship between tan \(\theta\), sin \(\theta\), and cos \(\theta\)?

Q 08 What is cosec\(\ \theta\)?

Q 09 What is sec \(\theta\)?

Q 10 What is cot \(\theta\)?

Q 11 What are the stan dard trigonometric values of 0\(^\circ\), 30\(^\circ\), 45\(^\circ\), 60\(^\circ\), and 90\(^\circ\)?

Q 12 Why are trigonometric ratios importan t?

Q 13 What is an angle of elevation?

Q 14 What is an angle of depression?

Q 15 What is the Pythagorean identity in trigonometry?

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INTRODUCTION TO TRIGONOMETRY – Learning Resources

Detailed Notes

True / False

NCERT Solutions

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