Re: [中學] 三角函數
※ 引述《sheep7940807 (焦糖瑪琪朵)》之銘言：
: o o o n
: sin(1 ) x sin(3 ) x … x sin(89 )=2 ，求n=?
: 答案:n=-89/2
: 請問各位大大該怎麼做呢？
o o o o o o
先寫成 sin(1 ) x cos(1 ) x sin(3 ) x cos(3 ) … x sin(43 ) x cos(43 )
22 o o o o
= (1/2) [sin(2 ) x sin(6 ) x ‧‧‧x sin(86 )] x sin(45 )
o o
{利用 sinA x sin(60 - A) x sin(60 + A) = 1/4 sin(3A)}
22 7 o o o o
= (1/2) {(1/4) [sin(6 ) x .... x sin(78 )] x sin(30 )} x sin(45 )
37 o o o o
= (1/2) x sin(45 ) x [sin(6 ) x sin(18 ) x .... x sin(78 )]
-75/2 2 o o o
= (2) {(1/4) x sin(18 ) x sin(54 ) x sin(30 )}
-85/2 o o
= (2) x sin(18 ) x sin(54 )
-89/2
= (2)
故 n=-89/2
(呼!!!! 打得好累......)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 118.171.79.251
※ 編輯: jimmy451399 來自: 118.171.79.251 (10/20 22:13)
討論串 (同標題文章)
