Re: [中學] 三角函數求值
※ 引述《bingogo (很想認識你)》之銘言：
: 令 W = cos(2π/17) + isin(2π/17)
: 求 (1) W + W^2 + W^4 + W^8 + W^9 + W^13 + W^15 + W^16
: (2) W^3 + W^5 + W^6 + W^7 + W^10 + W^11 + W^12 + W^14
: 希望高手幫忙解答，感謝!
令 Z1 = W + W^2 + W^4 + W^8 + W^9 + W^13 + W^15 + W^16
Z2 = W^3 + W^5 + W^6 + W^7 + W^10 + W^11 + W^12 + W^14
則 Z1 + Z2 = -1, 且 Z1 > 0，Z2 < 0
又 W^17 = 1
將 Z1 平方可得 Z1^2 = Z1 + 2 (Z2 + 3)
= Z1 + 2 (-1 - Z1 + 3)
所以 Z1^2 + Z1 - 4 = 0
同理 Z2^2 + Z2 - 4 = 0
因此 Z1 = (-1 + √17)/2 Z2 = (-1 - √17)/2
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 39.12.76.144
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1463495624.A.63C.html
推
05/19 01:17, , 1F
05/19 01:17, 1F
→
05/19 11:14, , 2F
05/19 11:14, 2F
→
05/19 11:17, , 3F
05/19 11:17, 3F
→
05/19 11:20, , 4F
05/19 11:20, 4F
推
05/19 12:31, , 5F
05/19 12:31, 5F
→
05/19 12:34, , 6F
05/19 12:34, 6F
→
05/19 12:34, , 7F
05/19 12:34, 7F
推
05/19 14:35, , 8F
05/19 14:35, 8F
推
05/19 23:24, , 9F
05/19 23:24, 9F
討論串 (同標題文章)