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Inverse Trigonometric Functions

Telangana Open School (TOSS) · Class 12 · Mathematics

Quick revision notes for Inverse Trigonometric Functions — Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

55 questions25 flashcards4 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?
Inverse Trigonometric Functions covers several key topics that are frequently asked in Telangana Open School (TOSS) Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Inverse Trigonometric Functions — Telangana Open School (TOSS) Class 12 Mathematics?
Understand the core concepts first, then work through the 55 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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