{"problem":{"name":"I. Rotation","description":{"content":"Ehsan loves geometry! Especially he likes to rotate points! Given a point in the plane, Ehsan likes to rotate it by _k_ degrees (counter-clockwise), around the origin. What is the result of this rota","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":65536},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF100I"},"statements":[{"statement_type":"Markdown","content":"Ehsan loves geometry! Especially he likes to rotate points!\n\nGiven a point in the plane, Ehsan likes to rotate it by _k_ degrees (counter-clockwise), around the origin. What is the result of this rotation?\n\n## Input\n\nA single integer _k_ (0 ≤ _k_ < 360) is given in the first line. Two integer numbers _x_ and _y_ are given in the second line ( - 1390 ≤ _x_, _y_ ≤ 1390).\n\n## Output\n\nWrite two numbers. The result of the rotation. Your answer must have a relative error less than 10 - 1.\n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"Ehsan 热爱几何！尤其是他喜欢旋转点！\n\n给定平面上的一个点，Ehsan 喜欢将其绕 #cf_span(class=[tex-font-style-underline], body=[origin]) 逆时针旋转 #cf_span[k] 度。旋转后的结果是什么？\n\n第一行给出一个整数 #cf_span[k]（#cf_span[0 ≤ k < 360]）。第二行给出两个整数 #cf_span[x] 和 #cf_span[y]（#cf_span[ - 1390 ≤ x, y ≤ 1390]）。\n\n请输出两个数，即旋转后的结果。你的答案的相对误差必须小于 #cf_span[10 - 1]。\n\n## Input\n\n第一行给出一个整数 #cf_span[k]（#cf_span[0 ≤ k < 360]）。第二行给出两个整数 #cf_span[x] 和 #cf_span[y]（#cf_span[ - 1390 ≤ x, y ≤ 1390]）。\n\n## Output\n\n请输出两个数，即旋转后的结果。你的答案的相对误差必须小于 #cf_span[10 - 1]。\n\n[samples]","is_translate":true,"language":"Chinese"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ k \\in \\mathbb{Z} $ with $ 0 \\leq k < 360 $ be the rotation angle in degrees.  \nLet $ (x, y) \\in \\mathbb{R}^2 $ be the coordinates of the point to be rotated about the origin.\n\n**Constraints**  \n$ -1390 \\leq x, y \\leq 1390 $\n\n**Objective**  \nCompute the rotated point $ (x', y') $ obtained by rotating $ (x, y) $ counter-clockwise by $ k $ degrees about the origin:  \n$$\n\\begin{aligned}\nx' &= x \\cos \\theta - y \\sin \\theta \\\\\ny' &= x \\sin \\theta + y \\cos \\theta\n\\end{aligned}\n$$  \nwhere $ \\theta = \\frac{\\pi k}{180} $ radians.  \n\nOutput $ (x', y') $ with relative error less than $ 10^{-1} $.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF100I","tags":["geometry","math"],"sample_group":[["90\n1 1","\\-1.00000000 1.00000000"],["180\n1 1390","\\-1.00000000 -1390.00000000"]],"created_at":"2026-03-03 11:00:39"}}