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Airida
1 month ago
9

Jika sin x = p, dengan x tumpul, maka cos(x + 60) =​

Mathematics
1 answer:
lawyer [12.5K]1 month ago
5 0

Menjawab:

[(√1-p²) -3√p] / 2

Proses yang dijelaskan langkah demi langkah:

Berdasarkan identitas trigonometri, ekspansinya adalah benar:

Cos (A + B) = cosAcosB-sinAsinB

Menggunakan rumus ini untuk mengembangkan cos (x + 60).

cos (x + 60) = cosxcos60 - sinxsin60

Dengan sinx = p, yang berarti berlawanan/sisi miring

opp = p, hyp = 1

adj² = 1²-p²

adj = √1-p²

Cos (x) = adj / hyp = √1-p² / 1

Cos (x) = √1-p²

Cos60 = 1/2 dan sin60 = √3 / 2

Substitusi nilai-nilai ini ke rumus

cos (x + 60) = cosxcos60 - sinxsin60

cos (x + 60) = √1-p² (1/2) - p (√3 / 2)

cos (x + 60) = (√1-p²) / 2 - √3p / 2

Temukan KPK tersebut

cos (x + 60) = [(√1-p²) -3√p] / 2

Dengan demikian, cos (x + 60) = [(√1-p²) -3√p] / 2

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