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Revision Notes
Inverse Trigonometric Functions — Revision Notes
Punjab Board · Class 12 · Mathematics
Inverse Trigonometric Functions revision notes for Punjab Board Class 12 Mathematics: 4 topics in quick points.
44 questions25 flashcards6 formulas & key relations5 concepts
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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 NotesKey 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 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.
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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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