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Omni-MATH / Let n be a positive integer, n≥2, and put θ=2π/n. Define points P_(k)=(k,0) in the xy-plane, for k=1,2,…,n. Let R_(k) be the map that rotates the plane counterclockwise by the angl…

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problem

Let nn be a positive integer, n≥2n \ge 2, and put θ=2π/n\theta = 2 \pi / n. Define points Pk=(k,0)P_k = (k,0) in the xyxy-plane, for k=1,2,…,nk = 1, 2 , \dots, n. Let RkR_k be the map that rotates the plane counterclockwise by the angle θ\theta about the point PkP_k. Let RR denote the map obtained by applying, in order, R1R_1, then R2,…R_2, \dots, then RnR_n. For an arbitrary point (x,y)(x,y), find, and simplify, the coordinates of R(x,y)R(x,y).
Plain-text mathematical notation (without MathML)
Let n be a positive integer, n≥2, and put θ=2π/n. Define points P_(k)=(k,0) in the xy-plane, for k=1,2,…,n. Let R_(k) be the map that rotates the plane counterclockwise by the angle θ about the point P_(k). Let R denote the map obtained by applying, in order, R₁, then R₂,…, then R_(n). For an arbitrary point (x,y), find, and simplify, the coordinates of R(x,y).
Original LaTeX notation
Let $n$ be a positive integer, $n \ge 2$, and put $\theta = 2 \pi / n$. Define points $P_k = (k,0)$ in the $xy$-plane, for $k = 1, 2 , \dots, n$. Let $R_k$ be the map that rotates the plane counterclockwise by the angle $\theta$ about the point $P_k$. Let $R$ denote the map obtained by applying, in order, $R_1$, then $R_2, \dots$, then $R_n$. For an arbitrary point $(x,y)$, find, and simplify, the coordinates of $R(x,y)$.

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Source and history

task_id
27653039-612d-5787-965b-6ea213f91950
task_key
test--27653039-612d-5787-965b-6ea213f91950
task_revision_id
1
config / split
/ test

Official source

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