Final answer:
The exact value of cos(θ/2) cannot be determined without specific information for the angle θ, but it is generally found using the half-angle formula involving cos(θ) if the angle's value or context is known.
Step-by-step explanation:
The question pertains to finding the exact value of cos(θ/2), where θ is an angle in the interval [0, 2π]. To determine this, we would typically use trigonometric identities or formulas specific to half-angle calculations. However, without a specific value or further context for θ, we cannot provide an exact value for cos(θ/2). If there were a typo and we had a specific value for θ, we would use the half-angle formula cos(θ/2) = ±√((1+cos(θ))/2), with the sign depending on the quadrant in which θ/2 lies.
If the given information was intended to provide an exact situation for a particular angle, such as from a diagram or an application in physics, then we would use the given ratios and relationships involving cos(θ) to find the needed values. In conclusion, without clearer information or a specific context, the exact value of cos(θ/2) cannot be determined from the information provided.