Final answer:
To solve i cos(cos⁻¹(-1/2)), find the angle whose cosine is -1/2, which is 2π/3 or 4π/3 (using principal value 2π/3), then substitute into the expression to get -i/2.
Step-by-step explanation:
The student is asking to find the trigonometric function with i cos(cos⁻¹(-1/2)). In trigonometry, the inverse cosine function cos⁻¹(x) returns the angle whose cosine is x. If x is -1/2, we are looking for an angle whose cosine is -1/2. Some angles that have a cosine of -1/2 are θ = 2π/3 or θ = 4π/3 (in radians). If we consider the principal value, cos⁻¹(-1/2) = 2π/3.
Knowing that, the original expression simplifies to i cos(2π/3). Now, cos(2π/3) = -1/2 (by unit circle definitions of cosine in the second quadrant), meaning the final answer would be i * (-1/2) or simply -i/2.