Answer: −π/6.
- A −π/6
- B π/6
- C −π/3
- D π/3
Correct answer: A. −π/6
Explanation: Since arcsine is odd and sin⁻¹(1/2) = π/6, we get sin⁻¹(−1/2) = −π/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.