Inverse of tan function
o
Thus , the graph of sec – 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 sec -1 function , then ( b , a ) becomes the corresponding point on the graph of inverse of sec function
Inverse of tan function
o Natural domain & Range of tan function : tan : R – { x : x = ( 2n + 1 ) π / 2 , n ∈ Z } → R o
o
If we restrict domain to [ -π / 2 , π / 2 ], then it becomes one-one & onto with range R .
Restricted domain & range of tan function , tan : [ -π / 2 , π / 2 ] → R o Restricted domain & range of tan -1 function , tan -1 : R à [ -π / 2 , π / 2 ]
o Actually , tan function restricted to any of the intervals [ −3π / 2 , -π / 2 ], to [ π / 2 , 3π / 2 ] etc ., is one-one & its range is R . Corresponding to each such interval , we get a branch of function tan – 1 . The branch with range , [ -π / 2 , π / 2 ], is called principal value branch o
If y = tan – 1 x , then tan y = x . Thus , the graph of tan – 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 tan -1 function , then ( b , a ) becomes the corresponding point on the graph of inverse of tan function