), ( π , π ) etc., is bijective and its range is R . Thus cot – can be defined as a function whose domain is the R and range as any of the INVERSE TRIGONOMETRIC FUNCTIONS intervals (– π , ), ( , π ), ( π , π ) etc. These intervals give different branches of the function cot – . The function with range ( , π ) is called the principal value branch of the function cot – .
We thus have cot – : R → ( , π ) The graphs of y = cot x and y = cot – x are given in Fig . (i), (ii). Fig . (i) Fig .
(ii) The following table gives the inverse trigonometric function (principal value branches) along with their domains and ranges. sin – [– , ] cos – [– , ] [ , π ] cosec – R – (– , ) – { } sec – R – (– , ) [ , π ] – { } tan – R cot – R ( , π )