Tentukan himpunan penyelesaian dari persamaan-persamaan trigonometri berikut! c. tan 6 x = tan 7 8 ∘ , 0 ∘ ≤ x ≤ 36 0 ∘

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Jawaban yang benar untuk pertanyaan tersebut adalah { 1 3 ∘ , 4 3 ∘ , 7 3 ∘ , 10 3 ∘ , 13 3 ∘ , 16 3 ∘ , 19 3 ∘ , 22 3 ∘ , 25 3 ∘ , 28 3 ∘ , 31 3 ∘ , 34 3 ∘ } Persamaan Trigonometri Dasar Ingat persamaan trigonometri dasar berikut: Jika tan x = tan α , nilai x = α + k ⋅ 18 0 ∘ . Diketahui tan 6 x = tan 7 8 ∘ , 0 ∘ ≤ x ≤ 36 0 ∘ maka tan 6 x 6 x x ​ = = = = ​ tan 7 8 ∘ 7 8 ∘ + k ⋅ 18 0 ∘ 6 ​ 6 ​ ( 1 3 ∘ + k ⋅ 3 0 ∘ ) ​ 1 3 ∘ + k ⋅ 3 0 ∘ ​ Sehingga diperoleh: k = 0 → x = 1 3 ∘ + 0 ⋅ 3 0 ∘ = 1 3 ∘ k = 1 → x = 1 3 ∘ + 1 ⋅ 3 0 ∘ = 4 3 ∘ k = 2 → x = 1 3 ∘ + 2 ⋅ 3 0 ∘ = 7 3 ∘ k = 3 → x = 1 3 ∘ + 3 ⋅ 3 0 ∘ = 10 3 ∘ k = 4 → x = 1 3 ∘ + 4 ⋅ 3 0 ∘ = 13 3 ∘ k = 5 → x = 1 3 ∘ + 5 ⋅ 3 0 ∘ = 16 3 ∘ k = 6 → x = 1 3 ∘ + 6 ⋅ 3 0 ∘ = 19 3 ∘ k = 7 → x = 1 3 ∘ + 7 ⋅ 3 0 ∘ = 22 3 ∘ k = 8 → x = 1 3 ∘ + 8 ⋅ 3 0 ∘ = 25 3 ∘ k = 9 → x = 1 3 ∘ + 9 ⋅ 3 0 ∘ = 28 3 ∘ k = 10 → x = 1 3 ∘ + 10 ⋅ 3 0 ∘ = 31 3 ∘ k = 11 → x = 1 3 ∘ + 11 ⋅ 3 0 ∘ = 34 3 ∘ Dengan demikian, himpunan penyelesaiannya adalah { 1 3 ∘ , 4 3 ∘ , 7 3 ∘ , 10 3 ∘ , 13 3 ∘ , 16 3 ∘ , 19 3 ∘ , 22 3 ∘ , 25 3 ∘ , 28 3 ∘ , 31 3 ∘ , 34 3 ∘ } .