Inverse Trigonometric Function
1.0 Introduction
1.0 Introduction
In the previous chapter, we have studied about trigonometric functions i.e., $\sin x$, $\cos x$, $\tan x$, $\operatorname{cosec} x$, $\sec x$ and $\cot x$.
We are also familiar with the domain, range, and inverse of a function. In this chapter, we apply the concepts studied in both the chapters and we shall study about the restrictions on domain and range of trigonometric functions which ensure the existence of their inverses which we called as Inverse Trigonometric Functions.
From previous chapter, we can summarize the domain and range of trigonometric functions as:
| Trigonometric function | Domain | Range |
| $\sin x$ | $R$ | $\left[ { - 1,1} \right]$ |
| $\cos x$ | $R$ | $\left[ { - 1,1} \right]$ |
| $\tan x$ | $R - \left\{ {\left( {2n + 1} \right)\frac{\pi }{2}} \right\}$ | $R$ |
| $\operatorname{cosec} x$ | $R - \left( {n\pi } \right)$ | $R - ( - 1,1)$ |
| $\sec x$ | $R - \left\{ {\left( {2n + 1} \right)\frac{\pi }{2}} \right\}$ | $R - ( - 1,1)$ |
| $\cot x$ | $R - \left( {n\pi } \right)$ | $R$ |
$$R \in {\text{Real number}}\quad {\text{and}}\quad n \in Z({\text{integer)}}$$
