Answer: -pi/3.
- A 2pi/3
- B -pi/3
- C pi/3
- D pi/6
Correct answer: B. -pi/3
Explanation: tan(2pi/3) = -sqrt(3). Since 2pi/3 is outside (-pi/2,pi/2), find principal value: tan-1(-sqrt3) = -pi/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.