Class 12 Maths Inverse Trigonometric Functions Inverse of Cosine function

Inverse of Cosine function

  • Natural domain & Range of cosine function, cosine : R→ [– 1, 1]
  • If we restrict domain to [0, π], then it becomes one-one & onto with range [– 1, 1].
  • Restricted domain & range of cosine function, cosine : [ 0, π ] → [– 1, 1]
  • Restricted domain & range of cos-1 function, cos-1 : [– 1, 1] à [ 0, π ]
  • Actually, cosine function restricted to any of the intervals [– π, 0], [π, 2π] , is one-one & its range is [–1, 1]. Corresponding to each such interval, we get a branch of function cos–1. The branch with range , [0, π ], is called principal value branch
  • If y = cos–1 x, then cos y = x.
  • Thus, the graph of cos–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 cosine function, then (b, a) becomes the corresponding point on the graph of inverse of cosine function

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