Answer: 2π/3.
- A 2π/3
- B π/3
- C −π/3
- D π/6
Correct answer: A. 2π/3
Explanation: cos⁻¹(−x) = π − cos⁻¹(x) = π − π/3 = 2π/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.