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Inverse Trigonometric Functions — Revision Notes

ICSE · Class 12 · Mathematics

Inverse Trigonometric Functions revision notes for ICSE Class 12 Mathematics: 4 topics in quick points. Part of the ICSE Class 12 Mathematics syllabus.

104 questions30 flashcards22 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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Key Topics to Revise

1

1. Why inverse trigonometric functions are defined

  • Trigonometric functions repeat their values after fixed intervals, so they are neither one-one nor onto on their natural domains.
  • A function has an inverse only when it is a bijection.
  • Inverse trigonometric functions are built by restricting the domain and co-domain of the original trigonometric functions.
2

2. Principal value branches and basic identities

  • sin^-1 has principal range [-π/2, π/2].
  • cos^-1 has principal range [0, π].
  • tan^-1 has principal range (-π/2, π/2).
3

3. Negative argument and complementary angle properties

  • sin^-1, tan^-1, and cosec^-1 are odd in the inverse sense.
  • cos^-1, cot^-1, and sec^-1 satisfy supplementary-angle type identities.
  • Pairs such as sin^-1 x + cos^-1 x add to π/2.
4

4. Conversion among inverse trig functions

  • A right triangle gives direct conversion between all six inverse trig functions.
  • Theorem 4.9 converts sin^-1, cos^-1, and tan^-1 into each other.
  • Theorem 4.10 converts cosec^-1 and sec^-1 into sin^-1 and cos^-1 without case split.

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Full Notes

Key Concepts

Trigonometric functions are periodicThe principal value branches are sin^sin(sin^sin^Odd properties

Frequently Asked Questions

What are the important topics in Inverse Trigonometric Functions for ICSE Class 12 Mathematics?
Key topics in Inverse Trigonometric Functions include Why inverse trigonometric functions are defined, Principal value branches and basic identities, Negative argument and complementary angle properties, Conversion among inverse trig functions. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How should I revise Inverse Trigonometric Functions for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 104 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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