Answer: 5π/6.
- A 7π/6
- B 5π/6
- C π/6
- D −5π/6
Correct answer: B. 5π/6
Explanation: 7π/6 lies outside [0, π]; the principal value is 2π − 7π/6 = 5π/6.
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.