返回题库

HMMT 二月 2001 · 团队赛 · 第 5 题

HMMT February 2001 — Team Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Find all x between − and such that 1 − sin x − cos x = . 2 2 16
解析
  1. Find all x between − and such that 1 − sin x − cos x = . 2 2 16 4 4 4 2 1 2 Solution: 1 − sin x − cos x = ⇒ (16 − 16 cos x ) − sin x − 1 = 0 ⇒ 16 sin x − 16 √ 2 2 1 3 16 sin x + 1 = 0. Use the quadratic formula in sin x to obtain sin x = ± . Since 2 4 √ 2 3 π 5 π cos 2 x = 1 − 2 sin x = ± , we get x = ± , ± . 2 12 12