Answer: [−π/2, π/2].
- A [−π/2, π/2]
- B [0, π] only
- C [−π, π] only
- D [0, 2π] only
Correct answer: A. [−π/2, π/2]
Explanation: The principal branch of arcsine is [−π/2, π/2].
The graph of sin⁻¹x is confined to a narrow domain [-1,1] (since sine itself only takes values in that range) and range [-π/2,π/2] (the principal value branch chosen to make sine one-one and invertible there).
Concept context
Restricting trig functions to make them invertible, the principal value branches of sin-inverse, cos-inverse, tan-inverse, and friends, and the key identities relating them.