all real numbers R – (– , ). Fig . (i) Thus cosec – can be defined as a function whose domain is R – (– , ) and range could be any of the intervals −− { } , − { } , { } −π etc. The function corresponding to the range { } − is called the principal value branch of cosec – .
We thus have principal branch as cosec – : R – (– , ) → { } − The graphs of y = cosec x and y = cosec – x are given in Fig . (i), (ii). Also, since sec x = cos x , the domain of y = sec x is the set R – { x : x = ( n + ) π , n ∈ Z } and range is the set R – (– , ). It means that sec (secant function) assumes all real values except – < y < and is not defined for odd multiples of π .
If we restrict the domain of secant function to [ , π ] – { π }, then it is one-one and onto with Fig . (i) Fig . (ii) INVERSE TRIGONOMETRIC FUNCTIONS its range as the set R – (– , ). Actually, secant function restricted to any of the intervals [– π , ] – { −π }, [ , ] – , [ π , π ] – { π } etc., is bijective and its range is R – {– , }.
Thus sec – can be defined as a function whose domain is R – (– , ) and range could be any of the intervals [– π , ] – { −π }, [ , π ] – { π }, [ π , π ] – { π } etc. Corresponding to each of these intervals, we get different branches of the function sec – . The branch with range [ , π ] – { π