Question

Tentukan himpunan penyelesaian dari setiap soal berikut:
Persamaan trigonometri sederhana

Answer 1

Verified answer

Persamaan Trigonometri

[6] tan x = -1 dalam interval 0 ≤ x ≤ π
tan x = tan (π - π/4)
tan x = tan 3π/4
x = 3π/4 + k.π
k = 0 ⇒ x = 3π/4
k = 1 ⇒ x = 7π/4 
∴ HP = {3π/4, 7π/4}

[7] cos x = ¹/₂ dalam interval 0° ≤ x ≤ 180°
cos x = cos 60°
Bagian-1
x = 60° + k.360°
k = 0 ⇒ x = 60°
Bagian-2
x = (360°- 60°) + k.360°
x = 300° + k.360°
k = 0 ⇒ x = 300° 
∴ HP = {60°, 300°}

[8] sin x = -¹/₂ dalam interval 0 ≤ x ≤ 3π/2
sin x = sin (π + π/6)
sin x = sin (7π/6)
Bagian-1
x = 7π/6 + k.2π
k = 0 ⇒ x = 7π/6
Bagian-2
x = (2π - π/6) + k.2π
x = 11π/6 + k.2π
k = 0 ⇒ x = 11π/6 tidak memenuhi karena di luar interval
∴ HP = {7π/6}

[9] cos x = ¹/₂  dalam interval 0 ≤ x ≤ 3π
cos x = cos π/3
Bagian-1
x = π/3 + k.2π
k = 0 ⇒ x = π/3
k = 1 ⇒ x = 7π/3
Bagian-2
x = (2π - π/3) + k.2π
x = 5π/3 + k.2π
k = 0 ⇒ x = 5π/3
k = 1 ⇒ x = 11π/3 tidak memenuhi karena di luar interval 
∴ HP = {π/3, 5π/3, 7π/3}