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HMMT 十一月 2009 · GEN1 赛 · 第 3 题

HMMT November 2009 — GEN1 Round — Problem 3

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 3 ] What is the period of the function f ( x ) = cos(cos( x ))?
解析

英文解析

  1. [ 3 ] What is the period of the function f ( x ) = cos(cos( x ))?
    Answer: π Since f ( x ) never equals cos(1) for x ∈ (0 , π ) but f (0) = cos(1), the period is at least π .
    However, cos( x + π ) = − cos( x ), so cos(cos( x + π )) = cos(cos( x )).