Tentukan nilai cos (18 derajat)
Misalkan A = 18°
5A = 90 °
2A = 90 – 3A
Sin 2A = Sin (90-3A) = Cos 3A
2 Sin A Cos A = 4Cos 3 A – 3 Cos A, Batalkan Cos A karena bukan nol.
2 Sin A = 4 Cos 2 A – 3 = 1 – 4 Sin 2 A
4 Sin 2 A + 2 Sin A – 1 = 0
(sin A=frac{-2pm sqrt{-4(4)-1}}{2(4)})
=>(sin A=frac{-2pm sqrt{4+16}}{8})
=> (sin A=frac{-2pm 2sqrt{5}}{8})
=>(sin A=frac{-1pm sqrt{5}}{4})
Sekarang sin 18° adalah positif, karena 18° terletak di kuadran pertama.
Jadi, sin 18° = sin A
=>(sin A=frac{sqrt{5}-1}{4})
Sekarang cos 18° = (1 – sin 2 18°), [Mengambil nilai positif, cos 18° > 0]
=> (cos 18=sqrt{frac{16-(5+1-2sqrt{5})}{16}})
=> (cos 18=sqrt{frac{10+2sqrt{5}}{16}})
=>(cos 18= frac{sqrt{10+2sqrt{5}}}{4})
Penyelesaian
(cos 18= frac{sqrt{10+2sqrt{5}}}{4})