Inverse of Cosine function o Natural domain & Range of cosine function , cosine : R→ [– 1 , 1 ]
Natural domain & Range of sine function , sine : R→ [– 1 , 1 ]
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If we restrict domain to [ −π / 2 , π / 2 ], then it becomes one-one & onto with range [– 1 , 1 ].
o Restricted domain & range of sine function , sine : [ −π / 2 , π / 2 ] → [– 1 , 1 ] o Restricted domain & range of sin -1 function , sine : [– 1 , 1 ] à [ −π / 2 , π / 2 ]
o Actually , sine function restricted to any of the intervals [ −3π / 2 , -π / 2 ], to [ π / 2 , 3π / 2 ] etc ., is one-one & its range is [– 1 , 1 ]. Corresponding to each such interval , we get a branch of function sin – 1 . The branch with range , [ −π / 2 , π / 2 ], is called principal value branch
o If y = sin – 1 x , then sin y = x .
Graph of an inverse function can be obtained from the corresponding graph of original function as a mirror image ( i . e ., reflection ) along the line y = x .
The graph of sin – 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 sine function , then ( b , a ) becomes the corresponding point on the graph of inverse of sine function
Inverse of Cosine function o Natural domain & Range of cosine function , cosine : R→ [– 1 , 1 ]