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Inverse Trigonometric Functions — Syllabus

Tamil Nadu Board · Class 12 · Mathematics

What Inverse Trigonometric Functions covers in Tamil Nadu Board Class 12 Mathematics: 4 topics, for the 2026-27 session.

45 questions26 flashcards5 formulas & key relations5 concepts

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A comprehensive table summarizing all six inverse trigonometric functions, their domains, and their principal value branches (ranges).
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4 Topics · Tamil Nadu Board Class 12 Mathematics · 2026-27

Topics in Inverse Trigonometric Functions

1

Fundamental Concepts: Periodicity, Odd/Even Functions, and Inverse Functions

  • A function f is periodic if f(x + p) = f(x) for some smallest positive p, called the period.
  • sin x, cos x, cosec x, sec x have period 2π; tan x and cot x have period π.
  • An odd function satisfies f(−x) = −f(x); its graph is symmetric about the origin.
2

Inverse Sine Function (sin⁻¹ x or arcsin x)

  • sin : [−π/2, π/2] → [−1, 1] is a bijection in the restricted domain.
  • sin⁻¹ : [−1, 1] → [−π/2, π/2] is the inverse sine function.
  • Domain of sin⁻¹ x: [−1, 1]; Range (principal values): [−π/2, π/2].
3

Inverse Cosine Function (cos⁻¹ x or arccos x)

  • cos : [0, π] → [−1, 1] is a bijection in the restricted domain.
  • cos⁻¹ : [−1, 1] → [0, π] is the inverse cosine function.
  • Domain of cos⁻¹ x: [−1, 1]; Range (principal values): [0, π].
4

Inverse Tangent Function (tan⁻¹ x or arctan x)

  • tan : (−π/2, π/2) → ℝ is a bijection in the principal domain.
  • tan⁻¹ : ℝ → (−π/2, π/2) — domain is ALL real numbers.
  • Range (principal values): open interval (−π/2, π/2).

Key Concepts

A function f is periodic ifThe inverse sine function is definedThe inverse cosine function is definedThe inverse tangent function is definedThe inverse cosecant function is defined

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Frequently Asked Questions

What are the important topics in Inverse Trigonometric Functions for Tamil Nadu Board Class 12 Mathematics?
Key topics in Inverse Trigonometric Functions include Fundamental Concepts: Periodicity, Odd/Even Functions, and Inverse Functions, Inverse Sine Function (sin⁻¹ x or arcsin x), Inverse Cosine Function (cos⁻¹ x or arccos x), Inverse Tangent Function (tan⁻¹ x or arctan x). Study these first, then practise questions on each for the Tamil Nadu Board Class 12 board exam.
How should I revise Inverse Trigonometric Functions for the Tamil Nadu Board Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Inverse Trigonometric Functions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Tamil Nadu Board Class 12 Mathematics Syllabus

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