Answer: pi - cos-1 x.
- A cos-1 x
- B -cos-1 x
- C pi - cos-1 x
- D pi + cos-1 x
Correct answer: C. pi - cos-1 x
Explanation: cos-1 is not odd; the correct identity is cos-1(-x) = pi - cos-1 x.
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.