Inverse of Cot function
Inverse of Cot function
o
o
o
Natural domain & Range of cot function , cot : R – { x : x = nπ , n ∈ Z } → R If we restrict domain to [ 0 , π ], then it becomes one-one & onto with range R Restricted domain & range of cot function , cot : [ 0 , π ] → R o Restricted domain & range of cot -1 function , cot -1 : R à [ 0 , π ]
o
Actually , cot function restricted to any of the intervals [– π , 0 ], [ π , 2π ] , is oneone & its range is R . Corresponding to each such interval , we get a branch of function cot – 1 . The branch with range , [ 0 , π ], is called principal value branch
o If y = cot – 1 x , then cot y = x .
o
Thus , the graph of cot – 1 function can be obtained from the graph of original function by interchanging x and y axes , i . e ., if ( a , b ) is a point on the graph of cot function , then ( b , a ) becomes the corresponding point on the graph of inverse of cot function