. Some Fundamental Concepts Definition . (Periodicity) A real valued function f is periodic if there exists a number p > such that for all x in the domain of f , x is in the domain of f and f x f x ( ) The smallest of all such numbers, is called the period of the function f . For instance, sin , cos , sec e ix cosec , are periodic functions with period p radians, whereas tan cot are periodic functions with period p radians.
m m m m m x m Inverse - - Inverse Trigonometric Functions Definition . (Odd and Even functions) A real valued function f is an even function if for all x in the domain of f , - x is also in the domain of f and f f x ( ) A real valued function f is an odd function if for all x in the domain of f , - x is also in the domain of f and f f x ( ) For instance, , sin , , tan cot cosec are all odd functions , whereas , cos sec are even functions . Remark The period of f g h ± is lcm{period of period of g h }, whenever they exist. For instance, the period of y is p and that of y is p .