Answer: -7/25.
- A -7/25
- B 7/25
- C 18/25
- D -18/25
Correct answer: A. -7/25
Explanation: Let θ=cos⁻¹(3/5), so cosθ=3/5 (θ∈[0,π], principal range). Apply cos2θ=2cos²θ−1=2(9/25)−1=18/25−25/25=−7/25. Since 2θ∈[0,2π], the result −7/25 is valid. Answer: −7/25.
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.