Answer: (-pi/2, pi/2).
- A [-pi/2, pi/2]
- B (-pi/2, pi/2)
- C [0, pi]
- D (0, pi)
Correct answer: B. (-pi/2, pi/2)
Explanation: tan-1 x has principal value branch (-pi/2, pi/2), open interval since tan is undefined at the endpoints, with domain all real numbers.
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.