restricted to any of the intervals 1 1 14 etc is bijective 2 2 2 2 2 and its range is R Thus tan can be defined as a function whose domain is R and 3 3 range could be any of the intervals 2 2 2 2 T intervals give different branches of the function tan The branch with range is called the principal value branch of the function tan We thus have tan R The graphs of the function y tan x and ytan x are giver 2 y tan x Fig 2 5 i T T 3 CANCER T TT 2 2 3 2 TI 21 T Rationalised 2023 24 3 t 2 2TT 2 1 T 2 and so on These 74 2 2 Fig 2 5 i ii Y 2 2 1 Fig 2 5 ii We know that domain of the cot function cotangent function is the set x x R and x n n Z and range is R It means that cotangent function is not defined for integral multiples of If we restrict the domain of cotangent function to 0 then it is bijective with and its range as R In fact cotangent function restricted to any of the intervals 0 0 2 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 cot R 0 The graphs of y cot x and y cot x are given in Fig 2 6 i ii 3T 2 TC 2 O Y y tan x T intervals 1 0 0 2 etc These intervals give different branches of the function cot The function with range 0 is called the principal value branch of the function cot We thus have 12 INVERSE TRIGONOMETRIC FUNCTIONS 25 republished T 2T 3 2 X