Answer: [−1, 1].
- A [−1, 1]
- B [0, 1]
- C all real numbers
- D [−π, π]
Correct answer: A. [−1, 1]
Explanation: Since sine only outputs values in [−1, 1], its inverse accepts inputs in [−1, 1].
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.