6.6.2 Menyelesaikan Persamaan Trigonometri (Pemfaktoran)

6.6.2 Menyelesaikan Persamaan Trigonometri (Pemfaktoran)

Contoh:

Cari semua sudut untuk 0° ≤ x ≤ 360° yang boleh selesaikan setiap persamaan trigonometri yang berikut.

(a) kot x = –2 kos x

(b) 3 sek x = 4 kos x

Penyelesaian:

(a)

kot x = –2 kos x

\frac{\cos x}{\sin x} = - 2 \cos x

kos x = –2 kos x sin x

kos x + 2 sin x kos x = 0

kos x (1 + 2 sin x ) = 0

kos x = 0

x= 90^o, 270^o

1 + 2 sin x= 0

sin x = –½

∠asas x = 30^o

x = (180^o + 30^o), (360^o – 30^o)

x = 210^o, 330^o

Oleh itu, x = 90^o, 210^o, 270^o, 330^o

(b)

\begin{array}{l} 3 sek x = 4 k o s x \\ \frac{3}{k o s x} = 4 k o s x \\ 3 = 4 k o s^{2} x \\ k o s^{2} x = \frac{3}{4} \\ k o s x = \pm \frac{\sqrt{3}}{2} \\ ∠ asas = 30^{\circ} \\ x = 30^{\circ}, (180^{\circ} - 30^{\circ}), (180^{\circ} + 30^{\circ}), (360^{\circ} - 30^{\circ}) \\ x = 30^{\circ}, 150^{\circ}, 210^{\circ}, 330^{\circ} \end{array}

(c)

\begin{array}{l} 16 \tan x = k o t x \\ 16 \tan x = \frac{1}{\tan x} \\ \tan^{2} x = \frac{1}{16} \\ \tan x = \pm \frac{1}{4} \\ ∠ asas = {14.04}^{\circ} \\ x = {14.04}^{\circ}, (180^{\circ} - {14.04}^{\circ}), \\ (180^{\circ} + {14.04}^{\circ}), (360^{\circ} - {14.04}^{\circ}) \\ x = {14.04}^{\circ}, {165.96}^{\circ}, {194.04}^{\circ}, {345.96}^{\circ} \end{array}