The value of sin⁻¹(cos(43π/5)) is:

The value of sin⁻¹(cos(43π/5)) is:

• A. 3π/5
• B. −π/10
• C. π/10
• D. −3π/5

Answer: C) π/10

Explanation: cos(43π/5) = cos(8π + 3π/5) = cos(3π/5) = cos(π−2π/5) = −cos(2π/5) = sin(π/2 − 2π/5)? No. Better: cos(3π/5) = sin(π/2 − 3π/5) = sin(−π/10). sin⁻¹(sin(−π/10)) = −π/10? Check principal value: sin⁻¹(sin θ) = θ if θ ∈ [−π/2, π/2]. −π/10 ∈ range. So answer is −π/10. But option 1 is −π/10, option 2 is π/10. We recompute cos(43π/5): 43π/5 = 8π + 3π/5. cos(3π/5) = cos108° = −cos72° = −sin18° = sin(−18°) = sin(−π/10). sin⁻¹(sin(−π/10)) = −π/10. So correct index 1.