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HMMT 二月 2002 · 冲刺赛 · 第 9 题

HMMT February 2002 — Guts Round — Problem 9

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [4] Find all values of x with 0 ≤ x < 2 π that satisfy sin x + cos x = 2. 1
解析
  1. Find all values of x with 0 ≤ x < 2 π that satisfy sin x + cos x = 2. 2 2 Solution: Squaring both sides gives sin x + cos x + 2 sin x cos x = 1 + sin 2 x = 2, so π 5 π x = , . 4 4