F.4 trigonometric functions

2009-12-29 5:50 am
(a)
Give that cos 36 = ( 1 + sin 18 ) / ( 1 + 2 sin 18 )
Prove that 4 sin^2 18 + 2 sin 18 -1 = 0 by using double angle forumulae of cosine.
(b)
Hence, find the value of sin 18.
更新1:

Please use cos 36 = ( 1 + sin 18 ) / ( 1 + 2 sin 18 ) and double angle forumulae of cosine.

回答 (2)

2009-12-29 5:57 am
✔ 最佳答案
cos 36 =1-2(sin 18)^2
So ( 1 + sin 18 ) / ( 1 + 2 sin 18 )=1-2(sin 18)^2
1+sin18=1-2(sin18)^2+2sin18-4(sin18)^3
4(sin18)^3+2(sin18)^2-sin18=0
(sin18)(4 sin^2 18 + 2 sin 18 -1)=0
4 sin^2 18 + 2 sin 18 -1 = 0 (sin sin18 <>0)

sin 18
=[-2+√(4+16)]/8
=[-1+√5]/4

2009-12-28 22:11:26 補充:
double angle forumulae of cosine !!!
2009-12-31 2:03 am


收錄日期: 2021-04-26 14:01:36
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091228000051KK01810

檢視 Wayback Machine 備份