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Formula Sheet

Inverse Trigonometric Functions — Formula Sheet

Punjab Board · Class 12 · Mathematics

6 formulas from Inverse Trigonometric Functions (Punjab Board Class 12 Mathematics) on one page, grouped by topic.

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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6 Entries · 4 Sections

Formulas and Key Relations

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

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.

Step-by-Step Method: Finding Principal Values

For negative values

use identities sin(-θ) = -sin θ, cos(π-θ) = -cos θ, tan(-θ) = -tan θ, cot(π-θ) = -cot θ.

Properties of Inverse Trigonometric Functions — Group 1: Reciprocal Relations

sin⁻¹(1/x) = cosec⁻¹(x) for |x| ≥ 1

cos⁻¹(1/x) = sec⁻¹(x) for |x| ≥ 1

Key relations

If y = cos⁻¹(x), then cos(y) = x and 0 ≤ y ≤ π.

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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 many formulas are in Inverse Trigonometric Functions?
This sheet lists 6 formulas from Inverse Trigonometric Functions, grouped by topic. Learn what each symbol stands for so you can apply the formula, not just recall it.
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.

More resources for Inverse Trigonometric Functions

All Punjab Board Class 12 Mathematics Formula Sheet

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