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Inverse Trigonometric Functions

Punjab Board · Class 12 · Mathematics

Quick revision notes for Inverse Trigonometric Functions — Punjab Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

44 questions25 flashcards5 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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Key Topics to Revise

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

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Full Notes

Key Concepts

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

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 Flowchart showing the process of creating an inverse trigonometric function through domain restriction, Visual representation of principal value branches for sin⁻¹ and cos⁻¹ functions, Comparison of key characteristics of tan⁻¹ and cot⁻¹ functions. These are the concepts Punjab Board Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Inverse Trigonometric Functions — Punjab Board Class 12 Mathematics?
Understand the core concepts first, then work through the 44 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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