Tentukan hp untuk 0°_< x _< 360 ° a.2 cosx + 2 sin x =√2 b.cos x - √3 sin x - 1=0 _< kurang dari

0° ≤ x ≤ 360°

*Menggunakan rumus
a sin x + b cos x = [tex] \sqrt{a^2+b^2} [/tex] sin (x - @)
dengan tan @ = b/a *

a)
2 cos x + 2 sin x = √2
[tex] \sqrt{2^2+2^2} [/tex] sin (x - @) = √2

*tan @ = 2/2 = 1 ; maka @ = 45° atau 225° *
(i)
2√2 sin (x - 45°) = √2
sin (x - 45°) = 1/2
sin (x - 45°) = sin 30°

x - 45° = 30° ± k.360°
x = 75° ± k.360°
x = 75°

x - 45° = (180°-30°) ± k.360°
x = 195° ± k.360°
x = 195°

(ii)
2√2 sin (x - 225°) = √2
sin (x - 225°) = 1/2
sin (x - 225°) = sin 30°
*sama*


b)
cos x - √3 sin x = 1
[tex] \sqrt{(-√3)^2+1^2} [/tex] sin (x - @) = 1
2 sin (x - @) = 1
sin (x - @) = 1/2

* tan @ = -√3/1 = -√3 ; maka @ = 120° atau @ = 300° *

(i)
sin (x - 120°) = sin 30°
x - 120° = 30° ± k.360°
x = 150° ± k.360°
x = 159°

(ii)
sin (x - 120°) = sin 30°
x - 120° = (180°-30°) ± k.360°
x = 270° ± k.360°
x = 270°