Answer: π/3.
- A 2π/3
- B π/3
- C −π/3
- D π/6
Correct answer: B. π/3
Explanation: Since 2π/3 lies outside [−π/2, π/2], arcsin(sin(2π/3)) = π − 2π/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.