Class 12 Mathematics — Chapter 2: INVERSE TRIGONOMETRIC FUNCTIONS
Chapter 2: INVERSE TRIGONOMETRIC FUNCTIONS is a chapter in Class 12 Mathematics (Part 1), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 7 topics including Conditions for Inverse Functions, Inverse Sine Function (sin⁻¹x), Inverse Cosine Function (cos⁻¹x). BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Conditions for Inverse Functionsone-oneontobijectiveinvertibledomain restriction
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▸Inverse Sine Function (sin⁻¹x)Core conceptinverse sinearcsindomainrangeprincipal value branch
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▸Inverse Cosine Function (cos⁻¹x)Core conceptinverse cosinearccosdomainrangeprincipal value branch
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▸Inverse Tangent Function (tan⁻¹x)Core conceptinverse tangentarctandomainrangeprincipal value branch
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▸Inverse Cosecant & Secant Functions (cosec⁻¹x, sec⁻¹x)Core conceptinverse cosecantarccscinverse secantarcsecprincipal value
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▸Summary of Domains and Principal Value RangesCore conceptdomainrangeprincipal valuesin⁻¹xcos⁻¹x
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▸Graphical Representation of Inverse Trigonometric Functionsgraphreflectiony = xmirror imageaxes
Chapter Summary
Understand why trigonometric functions, in their entirety, do not have inverses and why their domains must be restricted to make them one-one and onto (bijective) before an inverse can be defined.
Define the inverse sine function (arcsin x), its domain [-1, 1], and its principal value branch (range) which is [-π/2, π/2]. Understand that y = sin⁻¹x implies sin(y) = x.
Define the inverse cosine function (arccos x), its domain [-1, 1], and its principal value branch (range) which is [0, π].
Define the inverse tangent function (arctan x), its domain which includes all real numbers (R), and its principal value branch (range) which is (-π/2, π/2).
Define the inverse cosecant and secant functions, their common domain R – (–1, 1), and their respective principal value branches: [-π/2, π/2] – {0} for cosec⁻¹x and [0, π] – {π/2} for sec⁻¹x.
Memorize and be able to recall the specific domain and principal value range for each of the six inverse trigonometric functions. This is crucial for solving problems involving principal values.
Understand that the graph of an inverse function y = f⁻¹(x) is a reflection of the graph of the original function y = f(x) across the line y = x. Be able to recognize the shapes of the graphs for sin⁻¹x, cos⁻¹x, etc., within their principal value branches.
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Visualize inverse function graphs easily? Get Solution →
- Apply inverse trig to real life? Get Solution →
- Explore angles beyond a circle? Get Solution →
- What is the domain of the inverse sine function, sin⁻¹(x)? Get Solution →
- What is the range of the principal value branch of the inverse cosine function, cos⁻¹(x)? Get Solution →
- Which of the following represents the principal value branch range for the inverse tangent function, tan⁻¹(x)? Get Solution →
- What does the notation (sin x)⁻¹ represent? Get Solution →
- The value of an inverse trigonometric function that lies in the range of the principal branch is called the: Get Solution →
Did you know?
- 💡 Encryption and decryption are perfect real-world examples of functions and their inverses.
- 💡 Ancient civilizations used early forms of trigonometry for astronomy and navigation.
- 💡 The number Pi, central to circles, never repeats and goes on infinitely.
- 💡 Sound waves and light waves can be described using trigonometric functions.
- 💡 A mathematical function is like a machine that takes an input and gives exactly one output.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 7 key topics: Conditions for Inverse Functions, Inverse Sine Function (sin⁻¹x), Inverse Cosine Function (cos⁻¹x), Inverse Tangent Function (tan⁻¹x), Inverse Cosecant & Secant Functions (cosec⁻¹x, sec⁻¹x), and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 2: INVERSE TRIGONOMETRIC FUNCTIONS important for board exams?
Yes — Class 12 is a CBSE board exam year, and every NCERT chapter is part of the syllabus. Use BrainWeave's AI tutor to master this chapter, then practice with the auto-generated quizzes and mind maps.
Can I get NCERT solutions for this chapter in Hindi?
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