Answer:
θ = {0, π/2, π, 3π/2, 2π} . . . . choice B
Explanation:
In this equation, r will be a maximum where cos(4θ) is a maximum. That is where ...
4θ = 2kπ . . . . for some integer k
Dividing by 4 gives ...
θ = k(π/2)
θ = {0, π/2, π, 3π/2, 2π} . . . . matches choice B
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You will note that the graph also has extremes at odd multiples of π/4. These are the locations where cosine is a minimum and r is negative. It can be argued that r is not a maximum at those points.