Answer: 0.5.
- A 0.5
- B exactly 1
- C exactly 0
- D exactly 2
Correct answer: A. 0.5
Explanation: cos and cos⁻¹ are inverses, so cos(cos⁻¹(0.5)) = 0.5.
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.