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Concept Maps

Inverse Trigonometric Functions — Concept Maps

Tamil Nadu Board · Class 12 · Mathematics

3 concept maps of Inverse Trigonometric Functions for Tamil Nadu Board Class 12 Mathematics, each also written out as a text outline.

45 questions26 flashcards5 formulas & key relations5 concepts

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A comprehensive table summarizing all six inverse trigonometric functions, their domains, and their principal value branches (ranges).
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An illustration from Super Tutor's Inverse Trigonometric Functions chapter — alongside flashcards, concept maps and practice questions.

3 Concept Maps

Inverse Trigonometric Functions – Complete Chapter Overview

Inverse Trigonometric Functions – Complete Chapter Overview

The map in words

  • Inverse Trig Functions
    • Basics
      • Periodic Functions
        • Period of sin cos = 2pi
        • Period of tan cot = pi
      • Odd and Even
        • Odd sin tan cot cosec
        • Even cos sec
      • Inverse Function Concept
        • Restrict Domain
        • Bijection Required
        • Graph Reflection in y=x
    • Six Inverse Functions
      • sin inverse x
        • Domain -1 to 1
        • Range -pi/2 to pi/2
        • Odd Function
      • cos inverse x
        • Domain -1 to 1
        • Range 0 to pi
        • Neither Odd nor Even
      • tan inverse x
        • Domain all Reals
        • Range open -pi/2 to pi/2
        • Odd Function
      • cosec inverse x
        • Domain R minus open -1 to 1
        • Range -pi/2 to pi/2 minus 0
        • Odd Function
      • sec inverse x
        • Domain R minus open -1 to 1
        • Range 0 to pi minus pi/2
      • cot inverse x
        • Domain all Reals
        • Range open 0 to pi
        • Neither Odd nor Even
    • Key Properties
      • Property I
        • f inverse of f theta = theta in principal domain
      • Property II
        • f of f inverse x = x
      • Property III Reciprocal
        • sin inverse 1/x = cosec inverse x
        • cos inverse 1/x = sec inverse x
        • tan inverse 1/x = cot inverse x for x>0
      • Property IV Reflection
        • sin inverse -x = minus sin inverse x
        • cos inverse -x = pi minus cos inverse x
        • tan inverse -x = minus tan inverse x
      • Property V Cofunction
        • sin inverse + cos inverse = pi/2
        • tan inverse + cot inverse = pi/2
        • sec inverse + cosec inverse = pi/2
      • Property VI Addition
        • sin inverse x plus sin inverse y
        • cos inverse x plus cos inverse y
        • tan inverse x plus tan inverse y
      • Property VII Double Angle
        • 2 tan inverse x as tan inverse
        • 2 tan inverse x as sin inverse
        • 2 tan inverse x as cos inverse
      • Property X Triple Angle
        • 3 sin inverse x formula
        • 3 cos inverse x formula
    • Applications
      • Finding Principal Values
      • Solving Equations
      • Solving Inequalities
      • Integration Formulas
      • Proving Identities

Problem-Solving Flowchart for Inverse Trigonometric Functions

Problem-Solving Flowchart for Inverse Trigonometric Functions

The map in words

  • Problem with Inverse Trig Function
    • What type of problem?
      • Evaluate inverse at a value: Check if input is in domain
        • Yes, in domain: Find the angle in principal range
          • Return the angle
            • Final Answer
        • No, outside domain: Return undefined/no solution
      • Simplify inverse of trig: Check if angle is in principal range
        • Yes, in range: Direct evaluation
          • Return result
        • No, outside range: Use reduction formulas
      • Solve equation: Apply inverse to both sides
        • Simplify right side
          • Solve algebraic equation
            • Verify solution in domain
              • Check original equation
      • Find composition f(f⁻¹): Use fundamental property
        • Which type?
          • f(f⁻¹(x)): Returns x
            • Direct substitution
          • f⁻¹(f(x)): Returns x if x in principal domain
          • Otherwise: Reduce to principal domain
      • Apply formula: Identify which formula applies
        • Which formula?
          • Sum/Difference: Use addition formulas
            • Apply and simplify
          • Double Angle: Use 2θ formulas
          • Triple Angle: Use 3θ formulas
          • Cofunction: Use complementary relationships

Inverse Trigonometric Functions – Complete Overview

Inverse Trigonometric Functions – Complete Overview

The map in words

  • Inverse Trig Functions
    • Six Inverse Functions
      • sin inverse x
        • Domain minus1 to 1
        • Range minuspi over2 to pi over2
        • Odd Function
      • cos inverse x
        • Domain minus1 to 1
        • Range 0 to pi
        • Neither odd nor even
      • tan inverse x
        • Domain all reals
        • Range open minuspi2 to pi2
        • Odd Function
      • cosec inverse x
        • Domain abs x geq 1
        • Range minuspi2 to pi2 excluding 0
      • sec inverse x
        • Domain abs x geq 1
        • Range 0 to pi excluding pi2
      • cot inverse x
        • Domain all reals
        • Range open 0 to pi
    • Key Properties
      • Property I and II
        • Cancellation Rules
        • sin of sin inverse x equals x
        • sin inverse of sin x equals x only in range
      • Property III
        • Reciprocal Identities
        • sin inverse 1 over x equals cosec inverse x
      • Property IV
        • Reflection Identities
        • sin inverse minus x equals minus sin inverse x
        • cos inverse minus x equals pi minus cos inverse x
      • Property V
        • Cofunction Identities
        • sin inverse x plus cos inverse x equals pi over 2
        • tan inverse x plus cot inverse x equals pi over 2
      • Property VI
        • Addition Formulas
        • tan inverse x plus tan inverse y
      • Property VII
        • Double Angle Formulas
        • 2 tan inverse x forms
    • Graph Features
      • sin inverse
        • Increasing S shaped curve
        • Passes through origin
      • cos inverse
        • Decreasing curve
        • y intercept pi over 2
      • tan inverse
        • Horizontal asymptotes at pm pi over 2
        • Increasing through origin
    • Applications
      • Integral Calculus
        • Standard integrals
      • Solving Equations
        • Combining tan inverse terms
      • Right Triangle Method
        • Finding composite values

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Frequently Asked Questions

What are the important topics in Inverse Trigonometric Functions for Tamil Nadu Board Class 12 Mathematics?
Key topics in Inverse Trigonometric Functions include Fundamental Concepts: Periodicity, Odd/Even Functions, and Inverse Functions, Inverse Sine Function (sin⁻¹ x or arcsin x), Inverse Cosine Function (cos⁻¹ x or arccos x), Inverse Tangent Function (tan⁻¹ x or arctan x). Study these first, then practise questions on each for the Tamil Nadu Board Class 12 board exam.
What do the concept maps for Inverse Trigonometric Functions show?
The 3 maps show how the ideas in Inverse Trigonometric Functions connect: Inverse Trigonometric Functions – Complete Chapter Overview; Problem-Solving Flowchart for Inverse Trigonometric Functions. Each map is also written out as an outline on this page.
How should I revise Inverse Trigonometric Functions for the Tamil Nadu Board Class 12 board exam?
Learn the core ideas first, then work through the 45 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 Tamil Nadu Board Class 12 Mathematics Concept Maps

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