Class 11th Math-Unit 13 – Inverse Trigonometric Functions

Exercise 13.1

 Exercise 13.2

MCQ’s

Unit 13 of the Class 11th Mathematics syllabus introduces students to the concept of inverse trigonometric functions. This unit is crucial for understanding how to reverse the processes of trigonometric functions, enabling students to solve equations that involve these functions.

Key Topics Covered:

1. Introduction to Inverse Trigonometric Functions:
   • Definition and purpose of inverse trigonometric functions.
   • Explanation of how inverse functions help find angles when the values of trigonometric functions are known.
2. Notation and Representation:
   • Common notations used for inverse trigonometric functions, such as sin⁡−1x\sin^{-1} xsin−1x, cos⁡−1x\cos^{-1} xcos−1x, tan⁡−1x\tan^{-1} xtan−1x, and their reciprocals.
   • Graphical representation of these functions to understand their behavior and ranges.
3. Domains and Ranges:
   • Detailed discussion on the domains (input values) and ranges (output values) of inverse trigonometric functions.
   • Understanding how these ranges differ from the original trigonometric functions.
4. Properties of Inverse Trigonometric Functions:
   • Key properties and identities related to inverse functions, including:
     • sin⁡(sin⁡−1x)=x\sin(\sin^{-1} x) = xsin(sin−1x)=x
     • cos⁡(cos⁡−1x)=x\cos(\cos^{-1} x) = xcos(cos−1x)=x
     • tan⁡(tan⁡−1x)=x\tan(\tan^{-1} x) = xtan(tan−1x)=x
   • Other important relationships between the functions, such as sin⁡−1x+cos⁡−1x=π2\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}sin−1x+cos−1x=2π​.
5. Graphing Inverse Trigonometric Functions:
   • Techniques for graphing the inverse trigonometric functions, highlighting their unique characteristics compared to standard trigonometric graphs.
   • Analysis of symmetry and periodicity in these functions.
6. Applications:
   • Practical applications of inverse trigonometric functions in solving real-world problems, such as:
     • Finding angles in right triangles when the lengths of the sides are known.
     • Applications in physics, engineering, and computer graphics.
7. Solving Equations:
   • Methods for solving equations that involve inverse trigonometric functions.
   • Strategies for manipulating and simplifying expressions to find solutions.
8. Examples and Practice Problems:
   • A variety of examples to illustrate the concepts of inverse trigonometric functions.
   • Practice problems to reinforce understanding and mastery of the topic.

Conclusion:

Unit 13 on inverse trigonometric functions provides students with essential tools for working with angles and trigonometric values. Mastering this unit is crucial for further studies in mathematics, particularly in calculus and advanced algebra, as it lays the groundwork for understanding more complex functions and equations in future coursework.