Final answer:
None of the given options correctly represent a circle with a radius of 5/6 meters fitting the polar equation r=5/6cos(θ). The equation describes a circle that changes with cos(θ), and none of the options match this description.
Step-by-step explanation:
The experiment determines that the polar equation r=5/6cos(θ), where r is in meters, represents the greatest distance between two individuals that still allows them to hear each other speak. In order to determine which curve represents this scenario, let’s analyze the given options in terms of polar coordinates.
The equation r=5/6cos(θ) describes a circle in polar coordinates with a radius that changes depending on the angle θ. Since the cosine function oscillates between -1 and 1, the maximum value of r occurs when cos(θ) is 1 (or -1 for the negative radius), which means the maximum distance r can be is 5/6. Looking at the given options, we must find a circle whose radius matches this maximum distance.
Option A, a circle goes through (3.75, π/2) and (3.75, 3π/2), is incorrect because its radius (3.75 meters) does not match the equation.
Option B, a circle goes through (4, π/2) and (4, 3π/2), is also incorrect for the same reason.
Option C, a circle goes through (0,0) and (11,0) with an inner loop at (0,0), does not represent a circle in the traditional sense and also does not follow the given polar equation.
Option D describes a convex shape at (0,0) and thus would not represent a circle consistent with the polar equation given.
None of the options provided correctly represent a circle with a radius of 5/6 meters as described by the polar equation r=5/6cos(θ).