Answer: 3/4.
- A 3/4
- B 4/3
- C 3/5
- D 5/4
Correct answer: A. 3/4
Explanation: If theta = sin-1(3/5), then sin(theta)=3/5 and cos(theta) = 4/5 (right triangle with opposite 3, hyp 5, adjacent 4). tan(theta) = 3/4.
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.