1. Basic concepts , Domain and Range ,Principal Branch

Chapter-2

Inverse Trigonometric functions

Basic concepts , Domain and Range ,Principal Branch:

Let y = sinx        =>       x = sin^-1y

•  should not be confused with . In fact   
• i.e.,  ¹   
• And similarly for other trigonometric functions.
• The value of an inverse trigonometric functions which lies in its principal value branch is called the principal value of that inverse trigonometric functions.
• The domains and ranges (principal value branches) of inverse trigonometric functions are given in the following table:
• The functions

sin⁻¹x & tan⁻¹x

 are increasing functions in their domain.

• The functions

cos⁻¹x & cot⁻¹x

 are decreasing functions in over domain.

For suitable values of domain, we have

• 

•