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Inverse Trigonometric Functions — Revision Notes

Telangana Open School (TOSS) · Class 12 · Mathematics

Inverse Trigonometric Functions revision notes for Telangana Open School (TOSS) Class 12 Mathematics: 4 topics in quick points.

55 questions25 flashcards13 formulas & key relations4 concepts

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Key Topics to Revise

1

Understanding Inverse Trigonometric Functions

  • An inverse trigonometric function reverses the action of a trigonometric function.
  • Trigonometric functions are not one-to-one over their full domain, so we restrict domains to make them invertible.
  • The inverse function gives the angle corresponding to a given trigonometric ratio.
2

Domain and Range of Inverse Trigonometric Functions

  • Each inverse trigonometric function has a specific domain (allowed input values) and range (output angles).
  • The domain of sin⁻¹(x) and cos⁻¹(x) is [−1, 1], while their ranges differ.
  • tan⁻¹(x) and cot⁻¹(x) are defined for all real numbers but have different ranges.
3

Graphs of Inverse Trigonometric Functions

  • Graphs of inverse functions are reflections of original trigonometric graphs over the line y = x.
  • The graph of y = sin⁻¹(x) is increasing and lies between −π/2 and π/2.
  • y = cos⁻¹(x) decreases from π to 0 as x goes from −1 to 1.
4

Important Properties and Identities

  • Identities allow simplification of complex expressions involving multiple inverse functions.
  • sin⁻¹(x) + cos⁻¹(x) = π/2 for all x ∈ [−1, 1].
  • tan⁻¹(x) + cot⁻¹(x) = π/2.

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Full Notes

Key Concepts

The principal value of an inverseEach inverse trigonometric function hasImportant identities include sin⁻¹x + cos⁻¹xThe graphs of inverse trigonometric functions

Frequently Asked Questions

What are the important topics in Inverse Trigonometric Functions for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Inverse Trigonometric Functions include Understanding Inverse Trigonometric Functions, Domain and Range of Inverse Trigonometric Functions, Graphs of Inverse Trigonometric Functions, Important Properties and Identities. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Inverse Trigonometric Functions for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 55 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 Telangana Open School (TOSS) Class 12 Mathematics Revision Notes

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