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HMMT 十一月 2013 · 冲刺赛 · 第 15 题

HMMT November 2013 — Guts Round — Problem 15

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 9 ] Find all real numbers x between 0 and 360 such that 3 cos 10 = cos 40 + sin x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT NOVEMBER 2013, 9 NOVEMBER 2013 — GUTS ROUND
解析
  1. [ 9 ] Find all real numbers x between 0 and 360 such that 3 cos 10 = cos 40 + sin x . √ ◦ ◦ Answer: 70 , 110 (need both, but order doesn’t matter) Note that 3 = 2 cos 30 , so sin x = ◦ cos 20 = ⇒ x ∈ { 70 , 110 } .