Answer: 3pi/4.
- A pi/4
- B 3pi/4
- C -pi/4
- D pi/2
Correct answer: B. 3pi/4
Explanation: cot(3pi/4) = -1, and 3pi/4 lies in the principal range (0,pi), so cot-1(-1) = 3pi/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.