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2 sin x + √3 =0 ,0 <= x <= 2π
Jawaban:
Ingat!
Jika sin = sin α
Maka,
= α + k . 2π ...(1)
= (π- α) + k . 2π ...(2)
Diketahui,
2 sin - √3 = 0
Interval 0° ≤ ≤ 360°
Ditanyakan,
Himpunan penyelesaian
Dijawab,
2 sin - √3 = 0
2 sin = √3
sin = √3 /2
sin = sin 60°
sin = sin 1/3 π
= 1/3 π + k . 2π ...(1)
= (π-1/3 π) + k . 2π
= 2/3 π + k . 2π ... (2)
Interval 0° ≤ ≤ 360°
= 1/3 π + k . 2π ...(1)
Jika k = 0
= 1/3 π + 0 . 2π
= 1/3 π + 0
= 1/3 π
= 60°
Jika k = 1
= 1/3 π + 1 . 2π
= 1/3 π + 2π
= 1/3 π + 2.3/3π
= 1/3 π + 6/3π
= (1+6)/3 π
= 7/3 π
= 420° (tidak memenuhi)
= 2/3 π + k . 2π ... (2)
Jika k = 0
= 2/3 π + k . 2π
= 2/3 π + 0
= 2/3 π
= 120°
Jika k = 1
= 2/3 π + k . 2π
= 2/3 π + 1.2π
= 2/3 π + 2π
= 120° + 360°
= 480° (tidak memenuhi)
Sehingga dapat disimpulkan bahwa, himpunan penyelesaian dari 2 sin - √3 = 0 adalah {60°, 120°}.
Penjelasan dengan langkah-langkah:
selamat belajar ya jangan lupa folow dan bintang 5 ya
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