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Omni-MATH / The vertices of a regular hexagon are labeled cos(θ),cos(2θ),…,cos(6θ). For every pair of vertices, Bob draws a blue line through the vertices if one of these functions can be expr…

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problem

The vertices of a regular hexagon are labeled cos(θ),cos(2θ),…,cos(6θ)\cos (\theta), \cos (2 \theta), \ldots, \cos (6 \theta). For every pair of vertices, Bob draws a blue line through the vertices if one of these functions can be expressed as a polynomial function of the other (that holds for all real θ\theta ), and otherwise Roberta draws a red line through the vertices. In the resulting graph, how many triangles whose vertices lie on the hexagon have at least one red and at least one blue edge?
Plain-text mathematical notation (without MathML)
The vertices of a regular hexagon are labeled cos(θ),cos(2θ),…,cos(6θ). For every pair of vertices, Bob draws a blue line through the vertices if one of these functions can be expressed as a polynomial function of the other (that holds for all real θ ), and otherwise Roberta draws a red line through the vertices. In the resulting graph, how many triangles whose vertices lie on the hexagon have at least one red and at least one blue edge?
Original LaTeX notation
The vertices of a regular hexagon are labeled $\cos (\theta), \cos (2 \theta), \ldots, \cos (6 \theta)$. For every pair of vertices, Bob draws a blue line through the vertices if one of these functions can be expressed as a polynomial function of the other (that holds for all real $\theta$ ), and otherwise Roberta draws a red line through the vertices. In the resulting graph, how many triangles whose vertices lie on the hexagon have at least one red and at least one blue edge?

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Source and history

task_id
9c165e3f-aebc-5d89-b00b-f8b8b2613583
task_key
test--9c165e3f-aebc-5d89-b00b-f8b8b2613583
task_revision_id
1
config / split
/ test

Official source

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