Answer: 3π/4.
- A −π/4
- B 3π/4
- C π/4
- D −3π/4
Correct answer: B. 3π/4
Explanation: arccot has range (0, π); arccot(−1) = 3π/4.
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.