NCERT Exemplar Solutions Class 11 Maths Chapter 3 Trigonometric Functions

If you are preparing for the Class 11 Maths paper, Trigonometric Functions is the chapter you cannot afford to skip. It is the largest chapter in the whole Exemplar. The NCERT Exemplar Solutions for Class 11 Maths Chapter 3 Trigonometric Functions on this page solve all 76 questions of the chapter, step by step, according to the 2026-27 NCERT Exemplar.

Every solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT Exemplar, and checked line by line against the official answer key.

Chapter 3 has a single long exercise, Exercise 3.3, that mixes six question formats. The solutions PDF runs to 325 pages, the longest in the set, and covers all of them.

• 76 questions solved: Short Answer, Long Answer, Objective, Fill in the Blanks, True/False and Match the Following.
• Three printing errors flagged: the book is wrong on Q6, Q28 and Q29, each checked with a number.
• Exam focus: useful for CBSE Boards, JEE Main, JEE Advanced and CUET.

Topics Covered in the Class 11 Maths Trigonometric Functions Exemplar

Trigonometric Functions is the biggest chapter in the Exemplar because it carries the whole formula stack that later chapters reuse. Most questions are one formula plus one careful sign check. These are the topics the 76 questions are built on.

• Degrees, radians and minutes: converting between the three, where 30′ means half a degree, not 0.30 of one.
• Signs by quadrant: deciding the sign of a ratio from the quadrant, and halving an angle changes that quadrant.
• Sum and difference formulas: sin(A ± B), cos(A ± B) and tan(A ± B) applied to non-standard angles.
• Product-to-sum and sum-to-product: the four formulas that turn 2 sin A cos B into a sum, and back again.
• Multiple and half angles: sin 2x, cos 2x in its three forms, and the half-angle results.
• General solutions: the three families for sin, cos and tan equations, and knowing which one takes a ±.
• Range and maximum values: the range of expressions like a cos θ + b sin θ, and why sec²x has no upper bound.

Important: the three general-solution families are not interchangeable. A sine equation gives nπ + (−1)ⁿα, a cosine equation gives 2nπ ± α, and a tangent equation gives nπ + α with no ± at all. Mixing them is exactly the mistake the printed key makes twice in this chapter.

Exercise 3.3 Question-Type Breakdown for Trigonometric Functions

All 76 questions sit inside Exercise 3.3, grouped by format. The table below shows how the exercise is split, so students can plan practice by question type rather than solving straight through.

The Objective block (Q30 to Q59) is enormous. At 30 questions it is bigger than several whole chapters of the Exemplar, and it is where JEE-style range and maximum-value questions live. The Long Answer block is only 10 questions but takes the longest, because every general solution needs its family named and checked.

Three Printing Errors in the Trigonometric Functions Exemplar Every Student Must Know

The printed NCERT Exemplar for Chapter 3 is wrong on three questions. Two are wrong general solutions in the answer key. One is a misprinted question statement. Each is settled below by substituting a single number, so read this section before self-checking.

Q6 drops the halves from the question itself. Every angle on the left side carries a half: θ/2 and 9θ/2. So the honest right side is sin(8θ/2) sin(7θ/2), and the halves have been lost in printing. One number exposes it. Put θ = 0.3 radians: the left side gives 0.808, while sin 7θ sin 8θ gives 0.583. Two functions that disagree at a point are not the same function, so the printed identity cannot be proved as it stands.

Q28 puts a ± on a tangent equation. The equation reduces to tan 2x = 1, and a tangent equation always gives the single family X = nπ + α. The ± symbol belongs to the cosine family 2nπ ± α and to squared equations, never to a tangent. Test the key's minus branch at n = 0, so x = −π/8. The left side comes to about 2.66 and the right side to about 4.41. They differ by roughly 1.63, so −π/8 is simply not a root. The correct answer is x = nπ/2 + π/8.

Q29 gets the constant wrong twice over. The auxiliary angle π/12 must be subtracted, because it moves across the equals sign. And if you insist on writing the 2nπ ± form, the constant is not π/12 at all. Test the key at n = 0: it offers θ = π/4 + π/12 = π/3, and θ = −π/4 + π/12 = −π/6. Substituting gives 2.732 and −0.732, and neither is 2. The correct answer is θ = nπ + (−1)ⁿπ/4 − π/12.

Key Formulas Used in the Trigonometric Functions Exemplar

This chapter is the formula bank for the rest of Class 11 and 12 Maths. The Exemplar uses each of these many times over, so students should know them by heart before starting Exercise 3.3.

Tip: before proving any identity in this chapter, spot-check it with one convenient number. Put θ = 0.3 radians into both sides on a calculator. If the two sides disagree, the printed statement is wrong and no amount of algebra will fix it. That single habit catches the Q6 misprint in ten seconds.

Common Mistakes Students Make in the Trigonometric Functions Exemplar

With 76 questions, this chapter has more ways to lose a mark than any other. These five cost the most.

• Squaring without checking back. Squaring sin θ + cos θ = 1 gives roots including θ = π, where the left side is actually −1. Every squared root must be substituted back.
• Reading 30′ as 0.30 degrees. Minutes are sixtieths, not hundredths, so 22° 30′ is 22.5° and not 22.3°.
• Assuming θ/2 shares the quadrant of θ. It does not. A third-quadrant θ always gives a second-quadrant θ/2. Write the inequality and halve it on paper.
• Swapping the cosine and sine in sum-to-product. For a difference of sines the half-sum sits inside the cosine, not the sine.
• Clearing a denominator without a domain check. Multiplying through by cos x can create roots like x = 3π/2, where tan x and sec x are undefined.

Two of these are worth extra attention because they cost whole questions rather than single marks. The squaring trap appears in both the Long Answer and True/False blocks, and it is also why a substitution like y = sin²θ must carry its inherited range 0 ≤ y ≤ 1 on the same line. The general-solution family is the other one. Naming the wrong family costs the entire answer, and it is the mistake the printed key itself makes in Q28.

How the Trigonometric Functions Exemplar Steps Up from the NCERT Textbook

The Exemplar adds no new topics. It asks the same ideas in a harder way, as the table shows.

How to Use the Trigonometric Functions Exemplar for Boards and JEE Preparation

This is the longest chapter in the set, so five sittings work better than four. Finish the NCERT textbook exercises first, because the Exemplar assumes the formula stack is already memorised.

That is about 10 hours for the chapter, the largest single block in the Exemplar. For JEE Main and JEE Advanced, the 30-question Objective block is the best return on time, because range and maximum-value questions repeat almost every year. For CBSE Boards and CUET, the general solutions and the identity proofs matter more.

Practice Questions for Class 11 Maths Trigonometric Functions

After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Trigonometric Functions.

Other Resources for Class 11 Maths Trigonometric Functions

Pair the Exemplar Solutions with the textbook solutions and the notes for full chapter revision. All the Trigonometric Functions resources are linked below.

NCERT Exemplar Solutions for Other Class 11 Maths Chapters

The full Class 11 Maths Exemplar set covers 14 chapters, 735 questions and 2,625 pages of solutions. Use the table to jump to any other chapter.