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Inverse Trigonometric Functions

Tamil Nadu Board · Class 12 · Mathematics

Complete topic list for Inverse Trigonometric Functions in Tamil Nadu Board Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions26 flashcards5 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

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

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 Inverse Trigonometric Functions – Complete Chapter Overview, Problem-Solving Flowchart for Inverse Trigonometric Functions, Inverse Trigonometric Functions – Complete Overview. These are the concepts Tamil Nadu Board Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Inverse Trigonometric Functions — Tamil Nadu Board Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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 12 chapters — Tamil Nadu Board Class 12 Mathematics Syllabus

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