Tolong nomor 53 dan 54 beserta cara pengerjaan nya
Jawaban Terkonfirmasi
53) Tan 165° = Tan (120° + 45°)
= (Tan 120° + Tan 45°)/(1 – Tan 120° Tan 45°)
= (-√3 + 1) / (1 – (-√3)(1))
= (1 – √3)/(1 + √3) . (1 – √3)/(1 – √3)
= (1 – 2√3 + 3) / (1 – 3)
= (-2√3 + 4) / -2
= √3 – 2
54) y = 1/3 x^3 – 1/2 x^2 – x + 1
y' = x^2 – x – 1
m = y' => x^2 – x – 1 = 1
=> x^2 – x – 2 = 0
=> (x – 2)(x + 1) = 0
=> x = 2 atau x = -1
y = 1/3 x^3 – 1/2 x^2 – x + 1
x = 2 => y = 8/3 – 2 – 2 + 1 = 8/3 – 3 = -1/3
x = -1 => y = -1/3 – 1/2 + 1 + 1 = (-2 – 3 + 6 + 6)/6 = 7/6 = 1 1/6
Jadi ordinatnya adalah -1/3 dan 1 1/6