Using the identity cos 3A = 4(cosA)^3 - 3cosA , express sin 18° in surd form
Answer:
(-1+√5)/4
求詳細步驟
更新1:
數學代數三角比問題求解
數學代數二角比問題求解?
2018-06-14 5:30 pm
Given that sin 2θ = sin (90° - 3θ) when θ = 18°
Using the identity cos 3A = 4(cosA)^3 - 3cosA , express sin 18° in surd form
Answer:
(-1+√5)/4
求詳細步驟
Using the identity cos 3A = 4(cosA)^3 - 3cosA , express sin 18° in surd form
Answer:
(-1+√5)/4
求詳細步驟
回答 (1)
2018-06-14 5:50 pm
✔ 最佳答案
SolSin36°=Sin(90°－54°)
Sin36°=Cos54°
2sin18°Cos18°=4Cos^3 18°－3Cos18°
Cos18°<>0
2Sin18°=4Cos^2 18°－3
2Sin18°=4(1－Sin^2 18°)－3
2Sin18°=4－4Sin^2 18°－3
4Sin^2 18°+2Sin18°－1=0
Sin18°=[－2+√(2^2+4*4*1)]/8 (負不合)
Sin18°=(√5－1)/4
收錄日期: 2021-04-30 22:43:19
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