Answer: 2pi/3.
- A 4pi/3
- B 2pi/3
- C pi/3
- D -2pi/3
Correct answer: B. 2pi/3
Explanation: cos(4pi/3) = -1/2. Since 4pi/3 is outside [0,pi], we find the principal value: cos-1(-1/2) = 2pi/3.
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.