Inverse of Cot function
Inverse of Cot function
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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 ]
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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.
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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