Inverse of tan function
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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
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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