NCERT Class 12 Maths Inverse Trigonometric Functions

2.1 Introduction
In Chapter 1, we have studied that the inverse of a function f, denoted by f –1, exists if f is one-one and onto. There are many functions which are not one-one, onto or both and hence we can not talk of their inverses. In Class XI, we studied that trigonometric functions are not one-one and onto over their natural domains and ranges and hence their inverses do not exist. In this chapter, we shall study about the restrictions on domains and ranges of trigonometric functions which ensure the existence of their inverses and observe their behaviour through graphical representations. Besides, some elementary properties will also be discussed.

The inverse trigonometric functions play an important role in calculus for they serve to define many integrals. The concepts of inverse trigonometric functions is also used in science and engineering.

2.2 Basic Concepts
In Class XI, we have studied trigonometric functions, which are defined as follows:

             sine function, i.e., sine : R ® [– 1, 1]

             cosine function, i.e., cos : R ® [– 1, 1]

             tangent function, i.e., tan : R – { x : x = (2n + 1), π/2 ∈ Î Z} → R

             cotangent function, i.e., cot : R – { x : x = np, n ∈ Z} →R

             secant function, i.e., sec : R – { x : x = (2n + 1) 2/p , n Î Z} ® R – (– 1, 1)

             cosecant function, i.e., cosec : R – { x : x = np, n Î Z} ® R – (– 1, 1)

Please refer to attached file for NCERT Class 12 Maths Inverse Trigonometric Functions