Edzy
AI TutorResourcesToolsCompareBuy
SearchDownload AppLogin
Edzy

Edzy for Classes 6-12

Edzy is a personal AI tutor for CBSE and State Board students, with curriculum-aligned guidance, practice, revision, and study plans that adapt to each learner.

  • Email: always@edzy.ai
  • Phone: +91 96256 68472
  • WhatsApp: +91 96256 68472
  • Address: Sector 63, Gurgaon, Haryana

Follow Edzy

Browse by Class

  • CBSE Class 6
  • CBSE Class 7
  • CBSE Class 8
  • CBSE Class 9
  • CBSE Class 10
  • CBSE Class 11
  • CBSE Class 12
Explore the CBSE resource hub

Explore Edzy

  • Study Resources
  • Free Study Tools
  • Best Apps for Board Exams
  • Edzy vs ChatGPT
  • About Us
  • Why We Built Edzy
  • Blog
  • CBSE AI Tutor

Support & Legal

  • Help & FAQs
  • Accessibility
  • Privacy Policy
  • Terms & Conditions
  • Refund Policy
  • Cookie Policy
  • Site Directory

© 2026 Edzy. All rights reserved.

Curriculum-aligned learning paths for students in Classes 6-12.

Chapter Hub

Inverse Trigonometric Functions

This chapter on Inverse Trigonometric Functions discusses the conditions for the existence of inverse functions, their properties, and their graphical representations. It outlines their significance in calculus and applications in science and engineering.

Summary, practice, and revision
CBSE
Class 12
Mathematics
Mathematics Part - I

Inverse Trigonometric Functions

Chapter Summary

Playing 00:00 / 00:00

Download NCERT Chapter PDF for Inverse Trigonometric Functions – Latest Edition

Access Free NCERT PDFs & Study Material on Edzy – Official, Anytime, Anywhere

Live Challenge Mode

Ready to Duel?

Challenge friends on the same chapter, answer fast, and sharpen your concepts in a focused 1v1 battle.

NCERT-aligned questions
Perfect for friends and classmates

Why start now

Quick, competitive practice with instant momentum and zero setup.

More about chapter "Inverse Trigonometric Functions"

The chapter on Inverse Trigonometric Functions delves into the essential concepts and properties of inverse functions, particularly in the context of trigonometric functions. It explains how the existence of an inverse function requires the function to be one-one (bijective) and onto. Various trigonometric functions such as sine, cosine, and tangent are examined with their respective domains and ranges for defining their inverses. The chapter highlights the significance of principal value branches, demonstrated through graphical interpretations. The importance of these functions is amplified in calculus, serving as foundations for many integral definitions, and their relevance extends into various fields including science and engineering. Overall, this chapter serves to bridge the understanding between basic trigonometric functions and their inverses, preparing students for more advanced mathematical concepts.
Learn Better On The App
A clearer daily roadmap

Your Study Plan, Ready

Start every day with a clear learning path tailored to what matters next.

Daily plan
Less decision fatigue

Faster access to practice, revision, and daily study flow.

Edzy mobile app preview

Inverse Trigonometric Functions - Class 12 Mathematics

Explore the essential concepts of Inverse Trigonometric Functions, their properties, domains, and applications in calculus. Understand how to find and use these functions in real-world scenarios.

Inverse trigonometric functions are functions that return an angle whose trigonometric function yields a specific value. Examples include sin⁻¹(x), cos⁻¹(x), and tan⁻¹(x), which return angles corresponding to sine, cosine, and tangent values, respectively.
The domains of trigonometric functions are crucial for their inverses because a function must be one-one (bijective) to ensure that an inverse exists. Restrictions on the domains allow for unique angle outputs, thus defining the inverses accurately.
The principal value branch refers to the specific interval in which the inverse function is defined. For instance, the principal value branch for sin⁻¹(x) is typically restricted to [-π/2, π/2] to provide unique outputs for its inputs.
To find the inverse of the sine function, denoted as sin⁻¹(x), the domain is restricted to [-1, 1], resulting in outputs between [-π/2, π/2]. This ensures that each input corresponds to exactly one output angle.
The ranges for these functions are as follows: sin⁻¹(x): [-π/2, π/2]; cos⁻¹(x): [0, π]; tan⁻¹(x): (-π/2, π/2). These ranges ensure that each input yields a unique output.
Inverse functions are vital in calculus as they help define and solve integrals, particularly those involving trigonometric identities. Understanding these functions is essential for differentiating and integrating trigonometric expressions.
For example, to find the angle whose sine is 0.5, you would calculate sin⁻¹(0.5), which results in π/6. This helps solve various real-world applications like finding angles in triangles.
The relationship is defined as sin(sin⁻¹(x)) = x within the domain [-1, 1]. This means that applying the sine function to the arcsine of x returns x itself, serving as a verification of the inverse relationship.
To graph inverse trigonometric functions, reflect the graph of the original function across the line y = x. This visualizes the relationship between input values and angle outputs accurately.
The inverse cosine function, denoted as cos⁻¹(x), is typically defined over the interval [0, π]. This restriction ensures that every output angle is unique and covers the range of cosine values.
The value of π (approximately 3.14) is significant in trigonometry because it represents a complete revolution in radians. Many properties of trigonometric functions and their inverses are tied to angles measured in terms of π.
A function is one-one if every output is produced by exactly one input. For trigonometric functions, examining their behaviors and drawing their graphs can help identify intervals where they are bijective.
The domain of cosecant is all real numbers except where sine is zero (nπ, n ∈ Z), and the domain of secant excludes where cosine is zero ((2n + 1)π/2, n ∈ Z), which helps avoid undefined values.
Trigonometric functions like sine, cosine, and tangent are often paired with their respective inverses: arcsine, arccosine, and arctangent. They provide comprehensive tools for solving various equations and real-world problems.
To solve problems, express the given trigonometric equation in terms of an inverse function to find the angle. Then, use that angle to determine necessary distances or angles in application scenarios.
Inverse trigonometric functions are widely used in fields such as physics, engineering, and architecture to calculate angles for project designs, navigation, and resolving forces in mechanics.
Yes, the tangent function can have an inverse denoted as tan⁻¹(x), which is defined by restricting its domain to (-π/2, π/2), ensuring that it covers all real numbers uniquely.
Restricting the domain means limiting the values that the function can accept to ensure it is one-one, enabling the accurate definition of its inverse function without ambiguity.
Visualizing the relationship between a function and its inverse can be done by plotting both on the same graph and observing the symmetry across the line y = x, indicating their inverse nature.
The entire range isn't used because trigonometric functions are periodic and have multiple outputs for a single input. Hence, restricting the ranges to principal branches is necessary for defining unique inverses.
The sine and cosine functions are related through their inverses. For any angle θ, sin(θ) and cos(π/2 - θ) yield the same triangle ratios, making them functional inverses in certain trigonometric contexts.
When working with inverse trigonometric functions, it's important to assume that inputs lie within their defined domains, and outputs be interpreted only within the principal value branches for accuracy.

Chapters related to "Inverse Trigonometric Functions"

Relations and Functions

This chapter explores key concepts of relations and functions, including types of relations, properties of functions, and their compositions. Understanding these concepts is crucial for further studies in mathematics.

Start chapter

Matrices

This chapter introduces matrices, which are essential tools in various fields of mathematics and science. Understanding matrices helps simplify complex mathematical operations and solve systems of linear equations.

Start chapter

Determinants

This chapter covers determinants, their properties, and applications, which are essential for solving linear equations using matrices.

Start chapter

Continuity and Differentiability

This chapter covers important concepts of continuity and differentiability of functions. Understanding these topics is essential for further studies in calculus and mathematical analysis.

Start chapter

Application of Derivatives

This chapter explores how derivatives are applied in various fields such as engineering and science. It is crucial for understanding changes in values and optimizing functions.

Start chapter

Inverse Trigonometric Functions Summary, Important Questions & Solutions | All Subjects

Question Bank

Worksheet

Revision Guide

Formula Sheet