Pertanyaan

Himpunan penyelesaian dari persamaan sin ( x + 7 0 ∘ ) = sin 5 0 ∘ dengan 0 ∘ ≤ x ≤ 36 0 ∘ adalah ....

Himpunan penyelesaian dari persamaan $sin (x + 7 0^{\circ}) = sin 5 0^{\circ}$ dengan $0^{\circ} \leq x \leq 36 0^{\circ}$ adalah $....$

${2 0^{\circ}, 16 0^{\circ}}$
${5 0^{\circ}, 13 0^{\circ}}$
${5 0^{\circ}, 34 0^{\circ}}$
${6 0^{\circ}, 12 0^{\circ}}$
${6 0^{\circ}, 34 0^{\circ}}$

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Klaim

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Diketahui sin ( x + 7 0 ∘ ) = sin 5 0 ∘ maka sin ( x + 7 0 ∘ ) x + 7 0 ∘ x x = = = = sin 5 0 ∘ 5 0 ∘ 5 0 ∘ − 7 0 ∘ − 2 0 ∘ ± k ⋅ 36 0 ∘ Atau sin ( x + 7 0 ∘ ) sin ( x + 7 0 ∘ ) sin ( x + 7 0 ∘ ) x + 7 0 ∘ x x = = = = = = sin 5 0 ∘ sin ( 18 0 ∘ − 5 0 ∘ ) sin 13 0 ∘ 13 0 ∘ 13 0 ∘ − 7 0 ∘ 6 0 ∘ ± k ⋅ 36 0 ∘ x = − 2 0 ∘ ± k ⋅ 36 0 ∘ dan 0 ∘ ≤ x ≤ 36 0 ∘ maka k = 0 k = 1 x = − 2 0 ∘ ± k ⋅ 36 0 ∘ x = − 2 0 ∘ ± 0 ⋅ 36 0 ∘ x = − 2 0 ∘ ± 0 x = − 2 0 ∘ ( Tidakmemenuhi ) x = − 2 0 ∘ ± 1 ⋅ 36 0 ∘ x = − 2 0 ∘ ± 36 0 ∘ x = − 2 0 ∘ + 36 0 ∘ x = 34 0 ∘ x = − 2 0 ∘ − 36 0 ∘ x = − 38 0 ∘ ( Tidakmemenuhi ) x = 6 0 ∘ ± k ⋅ 36 0 ∘ dan 0 ∘ ≤ x ≤ 36 0 ∘ maka k = 0 k = 1 x = 6 0 ∘ ± k ⋅ 36 0 ∘ x = 6 0 ∘ ± 0 ⋅ 36 0 ∘ x = 6 0 ∘ ± 0 x = 6 0 ∘ x = 6 0 ∘ ± 1 ⋅ 36 0 ∘ x = 6 0 ∘ ± 36 0 ∘ x = 6 0 ∘ + 36 0 ∘ x = 42 0 ∘ ( Tidakmemenuhi ) x = 6 0 ∘ − 36 0 ∘ x = − 30 0 ∘ ( Tidakmemenuhi ) Jadi himpunan penyelesaian dari sin ( x + 7 0 ∘ ) = sin 5 0 ∘ adalah { 6 0 ∘ , 34 0 ∘ } . Oleh karena itu, jawaban yang tepat adalah E.

Diketahui $sin (x + 7 0^{\circ}) = sin 5 0^{\circ}$ maka

$sin (x + 7 0^{\circ}) x + 7 0^{\circ} x x = = = = sin 5 0^{\circ} 5 0^{\circ} 5 0^{\circ} - 7 0^{\circ} - 2 0^{\circ} \pm k \cdot 36 0^{\circ}$

Atau

$sin (x + 7 0^{\circ}) sin (x + 7 0^{\circ}) sin (x + 7 0^{\circ}) x + 7 0^{\circ} x x = = = = = = sin 5 0^{\circ} sin (18 0^{\circ} - 5 0^{\circ}) sin 13 0^{\circ} 13 0^{\circ} 13 0^{\circ} - 7 0^{\circ} 6 0^{\circ} \pm k \cdot 36 0^{\circ}$

$x = - 2 0^{\circ} \pm k \cdot 36 0^{\circ}$ dan $0^{\circ} \leq x \leq 36 0^{\circ}$ maka

$k = 0 k = 1 x = - 2 0^{\circ} \pm k \cdot 36 0^{\circ} x = - 2 0^{\circ} \pm 0 \cdot 36 0^{\circ} x = - 2 0^{\circ} \pm 0 x = - 2 0^{\circ} (Tidak memenuhi) x = - 2 0^{\circ} \pm 1 \cdot 36 0^{\circ} x = - 2 0^{\circ} \pm 36 0^{\circ} x = - 2 0^{\circ} + 36 0^{\circ} x = 34 0^{\circ} x = - 2 0^{\circ} - 36 0^{\circ} x = - 38 0^{\circ} (Tidak memenuhi)$

$x = 6 0^{\circ} \pm k \cdot 36 0^{\circ}$ dan $0^{\circ} \leq x \leq 36 0^{\circ}$ maka

$k = 0 k = 1 x = 6 0^{\circ} \pm k \cdot 36 0^{\circ} x = 6 0^{\circ} \pm 0 \cdot 36 0^{\circ} x = 6 0^{\circ} \pm 0 x = 6 0^{\circ} x = 6 0^{\circ} \pm 1 \cdot 36 0^{\circ} x = 6 0^{\circ} \pm 36 0^{\circ} x = 6 0^{\circ} + 36 0^{\circ} x = 42 0^{\circ} (Tidak memenuhi) x = 6 0^{\circ} - 36 0^{\circ} x = - 30 0^{\circ} (Tidak memenuhi)$