→ bibo9901 :x+y=π/4 => 0 <= x <= π/4 這行錯了 04/13 21:20
→ suker :y可以負值 有規定xy都正值? 04/13 21:33
→ hightacps :原來如此 想請問一下那行該如何改呢 從何而解?謝謝 04/13 23:14
推 qna :-1<=cos(x-π/8)<=1 04/13 23:33
推 G41271 :x可以是任意實數 04/13 23:57
x+y=π/4
則sinx + siny 的最小值為?
答案是-√[2-√(2)]
但我算法如下
y=π/4 - x
所以sinx + sin(π/4 - x) = 2sin(π/8)cos(x-π/8)=√[2-√(2)] cos(x-π/8)
而因為x+y=π/4 => 0 <= x <= π/4
=> -π/8<=x-π/8<=π/8
=> √[2+√(2)]/2<=cos(x-π/8) <=1
=> √(2)/2 <= √[2-√(2)] cos(x-π/8)<=√[2-√(2)]
算出來最小值是√(2)/2
請問我哪裡算錯呢
謝謝
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 112.104.86.187