Answer: pi/4.
- A 3pi/4
- B pi/4
- C -pi/4
- D pi/2
Correct answer: B. pi/4
Explanation: sin(3pi/4) = sin(pi/4) = 1/sqrt(2). Since 3pi/4 is outside [-pi/2,pi/2], the principal value is sin-1(1/sqrt2) = pi/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.