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Inverse Trigonometric Functions — Revision Notes

Madhya Pradesh Board · Class 12 · Mathematics

Inverse Trigonometric Functions revision notes for Madhya Pradesh Board Class 12 Mathematics: 4 topics in quick points.

105 questions44 flashcards6 formulas & key relations5 concepts

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A flowchart illustrating the conditions (one-one and onto) required for a function to have an inverse, and what happens if these conditions are not met.
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Key Topics to Revise

1

1. Basic ideas and principal value branches

  • A function has an inverse only when it is one-one and onto.
  • Sine, cosine, secant, cosecant, tangent, and cotangent are not one-one over their natural domains.
  • By restricting the domain, inverse trigonometric functions are defined.
2

2. Domains and principal value ranges

  • sin is one-one on [-π/2, π/2] and has range [-1, 1].
  • cos is one-one on [0, π] and has range [-1, 1].
  • cosec is one-one on [-π/2, π/2] - {0} and has range R - (-1, 1).
3

3. Standard principal values and worked examples

  • The principal value of sin⁻¹(1/√2) is π/4.
  • The principal value of cot⁻¹(-1/√3) is 2π/3.
  • For sin⁻¹(sin x), the answer must be reduced to the principal branch if needed.
4

4. Important identities and simplification patterns

  • Inverse trigonometric expressions are often simplified by substitution.
  • Trigonometric double-angle and triple-angle ideas are useful in inverse problems.
  • Some expressions become simple after using half-angle identities.

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Full Notes

Key Concepts

If f is oneThe value of an inverse trigonometricThe sine function restricted to [The cosine function restricted to [0cosec⁻¹x has domain R

Frequently Asked Questions

What are the important topics in Inverse Trigonometric Functions for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Inverse Trigonometric Functions include Basic ideas and principal value branches, Domains and principal value ranges, Standard principal values and worked examples, Important identities and simplification patterns. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How should I revise Inverse Trigonometric Functions for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 105 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 Madhya Pradesh Board Class 12 Mathematics Revision Notes

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