Answer: [0, π] excluding π/2.
- A [0, π]
- B [0, π] excluding π/2
- C [−π/2, π/2]
- D (0, π)
Correct answer: B. [0, π] excluding π/2
Explanation: arcsec takes values in [0, π] but never 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.