Final answer:
To find sin(2θ) given cos(θ), typically we'd use the double angle formula sin(2θ) = 2sin(θ)cos(θ). However, since cos(θ) = 61/60, which is greater than 1, θ is not a valid real angle. Thus, the problem as stated cannot be solved without correction or additional information.
Step-by-step explanation:
The question involves finding sin(2θ) given that cos(θ) = 61/60, which is not possible for a real angle θ since the cosine of an angle cannot exceed 1. However, assuming it's a theoretical or typo-related question, we would generally utilize trigonometric identities to find the value of sin(2θ).
Normally, the double angle formula for sine, which states sin(2θ) = 2sin(θ)cos(θ), would be used. However, since cos(θ) is already larger than 1, θ isn't a valid angle in real numbers, and thus the computation cannot proceed in the typical manner.
If we were to ignore the fact that cos(θ) cannot be greater than 1 and proceed purely algebraically, we would need the sine value of θ, which cannot be determined directly from the provided cos(θ) value because again, the value given violates the fundamental property of cos(θ) being at most 1. Therefore, in a real-world context, one cannot find sin(2θ) given cos(θ) = 61/60 without further information or a correction to the problem statement.
Given correct information, one would typically apply Pythagorean trigonometric identity, which is sin²(θ) + cos²(θ) = 1, to find sin(θ) and then apply double angle formula to find sin(2θ)