Chapter 2 of the Class 12 Maths is the Inverse Trigonometric Functions. It plays an important role in the calculus to find out the various integrals. These functions are useful in other areas of science and engineering. Students will get the knowledge of the restrictions on the domains and ranges of the trigonometric functions. These will ensure the existence of their inverses and observe their behaviour through the graphical representations. Besides this, some elementary properties are also very important and useful. Many suitable examples for Inverse Trigonometric Functions will be useful for the students.
The aim of this chapter is to make a student learn and get proficient in the understanding of basic concepts of trigonometry with inverse circular functions. Students who are learning these concepts will be able to learn about other related concepts of domain and the range of trigonometric functions. Further, they will also record their behaviour with the help of graphical representations.
The study of trigonometric functions was started in India from the period of Aryabhata. During the middle age, the study of trigonometry was continued in the Islamic Maths. The modern form of trigonometry functions was become popular since the 17th century by famous mathematician Isaac Newton and James Stirling etc.
We all know that a function will have the inverse if and only if it is one to one and onto both. Also, many functions are not one to one or onto because these functions are periodic. In order to get inverse of these functions, we need to restrict their domain and co-domain, so that they should become one to one and onto. Such restricted values are termed as principle values. Students must get complete practice and understanding of these inverse trigonometric functions with the domains and ranges. While solving the problems of this chapter students should keep in mind the value of inverse trigonometric functions and their principal value branches.
In the introduction, students will see the already learned functions and necessary conditions for the existence of their inverse functions. They will see the necessity and possibilities of defining an inverse trigonometric function.
In the basic concepts, students will get knowledge of trigonometric functions like sine, cosine, tangent, cot, cosec, sec. Also, the concept of an inverse trigonometric function with the procedure of finding the principal value of the inverse trigonometric function is important to learn. Besides the theoretical base and formulas, students will also learn the graphs of the inverse trigonometric functions.
In the section of properties of Inverse Trigonometric Functions, the student will understand the properties and the relationship between the various trigonometric functions in terms of formulae.
Therefore, it is necessary to practice all the NCERT textbook questions of this chapter to create a strong conceptual base. This chapter will definitely help the students to strengthen their foundation on the trigonometry. Also, these solutions will help with boosting the student confidence level for the current as well as further study. Thus the student must focus on this chapter and its findings. Many topics from Physics will be related to these concepts.