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HMMT 十一月 2013 · 冲刺赛 · 第 15 题

HMMT November 2013 — Guts Round — Problem 15

专题
Contest Math / 竞赛数学
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

英文原题

[ 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

英文解析

  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 } .