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標題:
Trigonometry
發問:
How to express cos 36 degree in surd form ? Please explain, thanks.
最佳解答:
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As cos 36°＝sin 54°, let θ＝18°, so,cos 2θ＝sin 3θ==> 1－2sin2θ＝3sin θ－4sin3θ==> 4sin3θ－2sin2θ－3sin θ＋1＝0==> (sin θ－1)(4sin2θ＋2sin θ－1)＝0==> sin θ＝1 or (-1＋√5)/4 or (-1－√5)/4As sin 18° has a positive value less than 1, so sin 18°＝(-1＋√5)/4,Therefore,cos 36°＝1－2sin218°＝1－2[(-1＋√5)/4]2＝1－(3－√5)/4＝(1＋√5)/4
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