Answer: π/3.
- A π/3
- B π/6
- C 2π/3
- D π
Correct answer: A. π/3
Explanation: Since π/3 lies in the principal range [−π/2, π/2], sin⁻¹(sin(π/3)) = π/3.
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.