Class 12 Maths Inverse Trigonometric Functions Inverse of Sin function

Inverse of Sin function

• Natural domain & Range of sine function, sine : R→ [– 1, 1]
• If we restrict domain to [−π/2, π/2 ], then it becomes one-one & onto with range [– 1, 1].
• Restricted domain & range of sine function, sine : [ −π/2, π/2 ] → [– 1, 1]
• Restricted domain & range of sin-1 function, sine : [– 1, 1] à [ −π/2, π/2 ]
• 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
• 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

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