Daftar Isi
HELP. Jika sin^2 x = akar 3 . cos x, maka cos x = ?
^ = pangkat
sin² x = √3. cos x
1- cos² x – √3 cos x = 0 atau
cos² x + √3. cos x = 1
(cos x + 1/2√3)² = 1 + 3/4 = 7/4
(cos x + 1/2 √3) = 1/2 √7
cos x = -1/2 √3 + 1/2 √7 = 1/2 (√7 – √3)
cos x = -1/2 √3 – 1/2 √7 = -1/2(√7 +√3)
tentukan nilai x dr : cos x – akar 3 . sin x = akar 2
cos x – √3 sin x = √2
<=> 1/2 cos x – 1/2 √3 sin x = 1/2 √2
<=> cos π/3 cos x – sin π/3 sin x = cos (π/4 + 2πk)
atau
cos π/3 cos x – sin π/3 sin x = cos (7π/4 + 2πk)
<=> cos (π/6 + x) = cos (π/4 + 2πk)
atau
cos (π/6 + x) = cos (7π/4 + 2πk)
<=> π/6 + x = π/4 + 2πk atau π/6 + x = 7π/4 + 2πk
<=> x = π/4 – π/6 + 2πk atau x = 7π/4 – π/6 + 2πk
<=> x = π/12 + 2πk atau x = 19π/12 + 2πk.
akar 3 cos x + sin x – akar 2 = 0
Jawab:
Trigonometri
Persamaan dlm bentuk a cos x + b sin x = k cos (x – a)
Penjelasan dgn langkah-langkah:
√3 cos x + sin x – √2 = 0
√3 cos x + sin x = √2
a= √3
b = 1
c= √2
.
ubah bentuk
√3 cos x + sin x = √2 –> k cos (x + α) =√2
k = √(a²+b²)
k = √(3+1)= 2
.
tan α = b/a = 1/√3 = tan 30
α = 30
.
√3 cos x + sin x = √2 –> 2 cos (x + 30) = √2
cos (x + 30)= 1/2 √2 = cos 45
x + 30 = 45 + k.360 atau x + 30 = – 45 + k. 360
x = 15 + k.360 atau x = -75 + k. 360
k = 0,1,2,3,….
.
k = 0 –> x = 15 atau x= -75
k = 1 –> x = 375 atau x = 285
.
HP untuk 0≤ x ≤ 360 –> x= (15, 285)
akar 3 sin x- cos x dapat ditulis dlm bentuk lain yaitu 2 cos…
a cos x + b sin x = k cos (x – α)
√3 sin x – cos x
a = -1
b = √3
a negatif b positif -> kuadran II
k² = a² + b²
k² = (-1)² + (√3)²
k² = 1 + 3
k² = 4
k = √4
k = 2
tan α = b/a
tan α = √3 / (-1)
tan α = -√3
tan α = -tan 60°
tan α = tan (180 – 60)°
tan α = tan 120°
α = 120°
maka
√3 sin x – cos x = 2 cos (x – 120)°
Cos (x+30derajat)=….
A.1/2akar3(cos x + sin x)
B.1/2akar3(cos x – sin x)
C.1/2(akar 3 cos x – sin x)
D.1/2 (cos x – akar 3 sin x)
E.1/2(cos x + akar 3 sin x)
mohon diperiksa kembali ya. 