Answer: -pi/2.
- A pi/2
- B -pi/2
- C pi
- D 0
Correct answer: B. -pi/2
Explanation: cosec(-pi/2) = -1, and -pi/2 lies in the principal range [-pi/2,pi/2] excluding 0, so cosec-1(-1) = -pi/2.
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.