P(cosθ,sinθ) cosθ sinθ θ
sin θ
Chapter 3  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Trigonometric Functions

The Highest-Yield Chapter — 35 Identities, Zero Excuses

📋 50 MCQs ⭐ 0 PYQs ⏱ 45 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
35Easy
10Medium
5Hard
0PYQs
45 secAvg Time/Q
4Topics
Easy 70% Medium 20% Hard 10%

Why Practise These MCQs?

JEE MainJEE AdvancedCBSEBITSATKVPY

This micro-bank of 50 MCQs focuses on NCERT-level trigonometric values, allied angles and basic identities — ideal for warm-up, speed drills, and error analytics before full -length JEE practice.

Topic-wise MCQ Breakdown

Values at Standard Angles22 Q
Allied Angles & Signs12 Q
Basic Identities10 Q
Simple Applications6 Q

Must-Know Formulae Before You Start

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

$sin²θ+cos²θ=1$
$sin(A±B)=sinA cosB ± cosA sinB$
$cos 2A = 1−2sin²A = 2cos²A−1$
$sin C+sin D = 2sin((C+D)/2)cos((C−D)/2)$
$tan(A+B) = (tanA+tanB)/(1−tanA·tanB)$

MCQ Solving Strategy

Never enter a trig MCQ without knowing which quadrant you are in — signs kill marks. For identity-based MCQs, reduce everything to sin and cos first. For equation MCQs, always write the general solution and then check which values fall in the given interval. Time-box trig MCQs at 90 seconds maximum.

⚠ Common Traps & Errors

Difficulty Ladder

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

① Easy

Standard angle values, unit circle quadrant signs, Pythagorean identity proofs

② Medium

Compound/double angle evaluation, graph reading, allied angle MCQs

③ Hard

Equation general solutions, multi-identity chains, KVPY conceptual

★ PYQ

JEE Main — 4–5 identity + equation MCQs; BITSAT — speed round

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Mathematical Induction MCQs
🎯 Knowledge Check

Maths — TRIGONOMETRIC FUNCTIONS

50 Questions Class 11 MCQs
1
The value of \( \sin 0^\circ \) is:
(NCERT–Basic)
2
The value of \( \cos 0^\circ \) is:
(NCERT–Basic)
3
The value of \( \tan 45^\circ \) is:
(NCERT–Basic)
4
The value of \( \sin 30^\circ \) is:
(NCERT–Basic)
5
The value of \( \cos 60^\circ \) is:
(NCERT–Basic)
6
The value of \( \sin 90^\circ \) is:
(NCERT–Basic)
7
The value of \( \cos 90^\circ \) is:
(NCERT–Basic)
8
The value of \( \tan 30^\circ \) is:
(NCERT–Basic)
9
The value of \( \tan 60^\circ \) is:
(NCERT–Basic)
10
The value of \( \sin 45^\circ \) is:
(NCERT–Basic)
11
The value of \( \cos 45^\circ \) is:
(NCERT–Basic)
12
The value of \( \sin(180^\circ - \theta) \) is:
(NCERT–Conceptual)
13
The value of \( \cos(180^\circ - \theta) \) is:
(NCERT–Conceptual)
14
The value of \( \sin(90^\circ - \theta) \) is:
(NCERT–Conceptual)
15
The value of \( \cos(90^\circ - \theta) \) is:
(NCERT–Conceptual)
16
The value of \( \tan(90^\circ - \theta) \) is:
(NCERT–Conceptual)
17
The value of \( \sin 270^\circ \) is:
(NCERT–Conceptual)
18
The value of \( \cos 270^\circ \) is:
(NCERT–Conceptual)
19
The value of \( \tan 180^\circ \) is:
(NCERT–Conceptual)
20
The value of \( \sin(-\theta) \) is:
(NCERT–Conceptual)
21
The value of \( \cos(-\theta) \) is:
(NCERT–Conceptual)
22
The value of \( \tan(-\theta) \) is:
(NCERT–Conceptual)
23
The value of \( \sin 150^\circ \) is:
(NCERT–Standard)
24
The value of \( \cos 150^\circ \) is:
(NCERT–Standard)
25
The value of \( \tan 150^\circ \) is:
(NCERT–Standard)
26
If \( \sin \theta = 3/5 \) and \( \theta \) is acute, then \( \cos \theta \) equals:
(NCERT–Application)
27
If \( \cos \theta = 12/13 \), then \( \sin \theta \) equals:
(NCERT–Application)
28
The value of \( \sin^2 30^\circ + \cos^2 30^\circ \) is:
(NCERT–Identity)
29
The value of \( \tan \theta \cdot \cot \theta \) is:
(NCERT–Identity)
30
The value of \( \sin 210^\circ \) is:
(NCERT–Advanced)
31
The value of \( \cos 210^\circ \) is:
(NCERT–Advanced)
32
The value of \( \tan 210^\circ \) is:
(NCERT–Advanced)
33
The value of \( \sin(360^\circ - \theta) \) is:
(NCERT–Advanced)
34
The value of \( \cos(360^\circ - \theta) \) is:
(NCERT–Advanced)
35
The value of \( \tan(360^\circ - \theta) \) is:
(NCERT–Advanced)
36
The value of \( \sin 300^\circ \) is:
(NCERT–Advanced)
37
The value of \( \cos 300^\circ \) is:
(NCERT–Advanced)
38
The value of \( \tan 300^\circ \) is:
(NCERT–Advanced)
39
The value of \( \sin 225^\circ \) is:
(NCERT–Advanced)
40
The value of \( \cos 225^\circ \) is:
(NCERT–Advanced)
41
The value of \( \tan 225^\circ \) is:
(NCERT–Advanced)
42
The value of \( \sin^2 45^\circ \) is:
(NCERT–Standard)
43
The value of \( \cos^2 60^\circ \) is:
(NCERT–Standard)
44
The value of \( \sin 0^\circ \cdot \cos 90^\circ \) is:
(NCERT–Standard)
45
The value of \( \tan 45^\circ + \cot 45^\circ \) is:
(NCERT–Standard)
46
The value of \( \sin 90^\circ \cdot \cos 0^\circ \) is:
(NCERT–Standard)
47
The value of \( \sin 120^\circ \) is:
(NCERT–Advanced)
48
The value of \( \cos 120^\circ \) is:
(NCERT–Advanced)
49
The value of \( \tan 120^\circ \) is:
(NCERT–Advanced)
50
The value of \( \sin 360^\circ \) is:
(NCERT–Advanced)
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Frequently Asked Questions

Trigonometrical functions are functions that relate an angle to ratios of sides of a right-angled triangle or to coordinates on the unit circle

Because each angle corresponds to a unique real value of sine, cosine, tangent, etc

An angle measured in radians can take any real value, positive or negative

Radian is the angle subtended at the center of a circle by an arc equal in length to the radius

There are p radians in 180 degrees

The domain of sin x and cos x is all real numbers

The range is from -1 to 1 inclusive

All real numbers except odd multiples of \(\pi/2\)

Periodicity means the function repeats its values after a fixed interval

The period is \(2\pi\)

The period is \(\pi)

Identities that hold true for all permissible values of \(x\), such as \(\sin^2 x + \cos^2 x = 1\)

Identities that relate trigonometric functions as reciprocals of each other

Identities expressing tan x and cot x as ratios of sine and cosine

Identities derived from the Pythagorean theorem involving sin, cos, and tan

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