Final answer:
The maximum value of r for the polar graph r = rcos⁵θ occurs at angles slightly less than whole multiples of π radians, however, they are still very close to these familiar values such as 0, π, 2π, and so forth.
Step-by-step explanation:
The student is asking about the location of the maximum value of r for the polar graph of the function r = rcos⁵θ. In polar coordinates, the maximum value of r would occur at angles where cosθ is maximum since raising a positive number to a power preserves the ordering. The maximum value of cosθ is 1, which occurs at θ = 0, θ = 2π, θ = 4π, and so on which are multiples of 2π radians. However, in context, since the radial function is a power of cos, the values at which maximum occur can be slightly less than whole multiples of π due to the contribution of higher powers of cosine. Still, the values would be very close to multiples of π radians.