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HMMT 二月 2008 · 冲刺赛 · 第 7 题

HMMT February 2008 — Guts Round — Problem 7

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] Given that x + sin y = 2008 and x + 2008 cos y = 2007, where 0 ≤ y ≤ π/ 2, find the value of x + y .
解析
  1. [ 6 ] Given that x + sin y = 2008 and x + 2008 cos y = 2007, where 0 ≤ y ≤ π/ 2, find the value of x + y . π Answer: 2007 + Subtracting the two equations gives sin y − 2008 cos y = 1. But since 0 ≤ y ≤ π/ 2, 2 the maximum of sin y is 1 and the minimum of cos y is 0, so we must have sin y = 1, so y = π/ 2 and π x + y = 2007 + . 2