Answer: 4/5.
- A 3/5
- B 4/5
- C 5/3
- D 5/4
Correct answer: B. 4/5
Explanation: If theta = cos-1(3/5), then cos(theta) = 3/5, so the opposite side is sqrt(25-9) = 4, giving sin(theta) = 4/5.
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.