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Inverse Trigonometric Functions — Syllabus

Punjab Board · Class 12 · Mathematics

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

44 questions25 flashcards6 formulas & key relations5 concepts

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A clear, organized comparison chart summarizing the domain and principal value range for all six inverse trigonometric functions: arcsin, arccos, arctan, arccosec, arcsec, and arccot.
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4 Topics · Punjab Board Class 12 Mathematics · 2026-27

Topics in Inverse Trigonometric Functions

1

Why Inverse Trigonometric Functions Are Needed

  • A function f has an inverse only if it is one-one (injective) AND onto (surjective), i.e., it must be bijective.
  • Trigonometric functions like sin, cos, tan are periodic and hence NOT one-one over their complete domains.
  • To define inverses, we RESTRICT the domain of each trigonometric function to a specific interval where it becomes one-one and onto.
2

Domains and Ranges of Inverse Trigonometric Functions (Principal Value Branches)

  • This table is the MOST IMPORTANT thing to memorise in this chapter — every problem requires knowing these domains and ranges.
  • sin⁻¹: Domain = [-1, 1], Range = [-π/2, π/2] — closed interval at both ends.
  • cos⁻¹: Domain = [-1, 1], Range = [0, π] — closed interval at both ends.
3

Step-by-Step Method: Finding Principal Values

  • Always follow the 3-step method: (1) Set the expression equal to y, (2) Rewrite as a trig equation, (3) Find y in the principal range.
  • Use standard trigonometric values: 0, π/6, π/4, π/3, π/2, 2π/3, 3π/4, 5π/6, π.
  • For negative values: use identities sin(-θ) = -sin θ, cos(π-θ) = -cos θ, tan(-θ) = -tan θ, cot(π-θ) = -cot θ.
4

Properties of Inverse Trigonometric Functions — Group 1: Reciprocal Relations

  • These properties connect inverse trig functions of reciprocals of arguments.
  • sin⁻¹(1/x) = cosec⁻¹(x) for |x| ≥ 1
  • cos⁻¹(1/x) = sec⁻¹(x) for |x| ≥ 1

Key Concepts

Trigonometric functions like sinThe function sin⁻¹The function cos⁻¹The function tan⁻¹cot⁻¹

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Frequently Asked Questions

What are the important topics in Inverse Trigonometric Functions for Punjab Board Class 12 Mathematics?
Key topics in Inverse Trigonometric Functions include Why Inverse Trigonometric Functions Are Needed, Domains and Ranges of Inverse Trigonometric Functions (Principal Value Branches), Step-by-Step Method: Finding Principal Values, Properties of Inverse Trigonometric Functions — Group 1: Reciprocal Relations. Study these first, then practise questions on each for the Punjab Board Class 12 board exam.
How should I revise Inverse Trigonometric Functions for the Punjab Board Class 12 board exam?
Learn the core ideas first, then work through the 44 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 Punjab Board Class 12 Mathematics Syllabus

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