Tentukan himpunan penyelesaian dari persamaan-persamaan trigonometri berikut! b. cos 4 x = − 2 1 ​ 3 ​ , 0 ∘ ≤ x ≤ 2 π

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Jawaban yang benar untuk pertanyaan tersebut adalah HP = { ​ ​ 24 5 ​ π , ​ ​ ​ 24 7 ​ ​ ​ ​ π ​ ​ ​ , ​ ​ ​ ​ ​ ​ 24 17 ​ π , ​ ​ ​ 24 19 ​ ​ ​ ​ π ​ ​ ​ , ​ ​ ​ ​ ​ ​ 24 29 ​ π , ​ ​ ​ 24 31 ​ ​ ​ ​ π ​ ​ ​ , ​ ​ ​ ​ ​ ​ 24 41 ​ π , 24 43 ​ π , ​ ​ ​ 24 53 ​ π } ​ . Ingat cos x = a diubah dahulu menjadi cos x = cos α . Jika cos x = cos α , maka x = α + k ⋅ 2 π atau x = − α + k ⋅ 2 π Diketahui cos 4 x = − 2 1 ​ 3 ​ untuk 0 ∘ ≤ x ≤ 2 π , maka cos 4 x cos 4 x ​ = = = = ​ − 2 1 ​ 3 ​ ( K . II / III ) cos ( 18 0 ∘ − 3 0 ∘ ) cos 15 0 ∘ cos 6 5 ​ π ​ Berdasarkan rumus di atas, dapat ditentukan: 4 x x x ​ = = = ​ 6 5 ​ π + k ⋅ 2 π 24 5 ​ π + k ⋅ 4 2 ​ π 24 5 ​ π + k ⋅ 2 1 ​ π ​ untuk k bilangan bulat, maka k k k k k ​ = = = = = ​ 0 , x = 24 5 ​ π + 0 ⋅ 2 1 ​ π = 24 5 ​ π ( memenuhi ) 1 , x = 24 5 ​ π + 1 ⋅ 2 1 ​ π = 24 17 ​ π ( memenuhi ) 2 , x = 24 5 ​ π + 2 ⋅ 2 1 ​ π = 24 29 ​ π ( memenuhi ) 3 , x = 24 5 ​ π + 3 ⋅ 2 1 ​ π = 24 41 ​ π ( memenuhi ) 4 , x = 24 5 ​ π + 4 ⋅ 2 1 ​ π = 24 53 ​ π ( tidak memenuhi ) ​ 4 x x x ​ = = = ​ − 6 5 ​ π + k ⋅ 2 π − 24 5 ​ π + k ⋅ 4 2 ​ π − 24 5 ​ π + k ⋅ 2 1 ​ π ​ untuk k bilangan bulat, maka k k k k k k ​ = = = = = = ​ 0 , x = − 24 5 ​ π + 0 ⋅ 2 1 ​ π = − 24 5 ​ π ( tidak memenuhi ) 1 , x = − 24 5 ​ π + 1 ⋅ 2 1 ​ π = 24 7 ​ π ( memenuhi ) 2 , x = − 24 5 ​ π + 2 ⋅ 2 1 ​ π = 24 19 ​ π ( memenuhi ) 3 , x = − 24 5 ​ π + 3 ⋅ 2 1 ​ π = 24 31 ​ π ( memenuhi ) 4 , x = − 24 5 ​ π + 4 ⋅ 2 1 ​ π = 24 43 ​ π ( memenuhi ) 5 , x = − 24 5 ​ π + 5 ⋅ 2 1 ​ π = 24 55 ​ π ( tidak memenuhi ) ​ Dengan demikian, HP = { ​ ​ 24 5 ​ π , ​ ​ ​ 24 7 ​ ​ ​ ​ π ​ ​ ​ , ​ ​ ​ ​ ​ ​ 24 17 ​ π , ​ ​ ​ 24 19 ​ ​ ​ ​ π ​ ​ ​ , ​ ​ ​ ​ ​ ​ 24 29 ​ π , ​ ​ ​ 24 31 ​ ​ ​ ​ π ​ ​ ​ , ​ ​ ​ ​ ​ ​ 24 41 ​ π , 24 43 ​ π , ​ ​ ​ 24 53 ​ π } ​ .