Skip to main content
Super TutorResources
Chapter 7 of 12
Revision Notes

Inverse Trigonometric Functions — Revision Notes

Tamil Nadu Board · Class 12 · Mathematics

Inverse Trigonometric Functions revision notes for Tamil Nadu Board Class 12 Mathematics: 4 topics in quick points.

45 questions26 flashcards5 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Inverse Trigonometric Functions? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

Free trial, no card needed.

A comprehensive table summarizing all six inverse trigonometric functions, their domains, and their principal value branches (ranges).
Super Tutor

An illustration from Super Tutor's Inverse Trigonometric Functions chapter — alongside flashcards, concept maps and practice questions.

Key Topics to Revise

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).

Get complete notes with diagrams and examples

Full Notes

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

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.

More resources for Inverse Trigonometric Functions

All Tamil Nadu Board Class 12 Mathematics Revision Notes

For serious students

Get the full Inverse Trigonometric Functions chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for Tamil Nadu Board Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free