In a beehive, each cell is a regular hexagonal prism, as shown in the figure. The amount of wax W in the cell depends on the apex angle θ and is given by W = 3.02 − 0.38 cot θ + 0.65 csc θ Bees instinctively choose θ so as to use the least amount of wax possible. For what value of θ does W have its minimum value?
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
In a beehive, each cell is a regular hexagonal prism, as shown in the figure. The amount of wax W in the cell depends on the apex angle θ and is given by
W = 3.02 − 0.38 cot θ + 0.65 csc θ
Bees instinctively choose θ so as to use the least amount of wax possible.
For what value of θ does W have its minimum value?
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