Answer:
<em>x = 15°</em>
<em>x = 135°</em>
<em>x = -45°</em>
<em>x = -180°</em>
Step-by-step explanation:
<u>Trigonometric Equations</u>
Solve
cos(2x + 30°) = 0.5 for -180° ≤ x ≤ 180°
Applying the inverse cosine function:
2x + 30° = arccos(0.5)
There are several angles whose cosine is 0.5. They are 60°, 300°, -60° and -300°, thus we have these candidate solutions:
2x + 30° = 60°
2x + 30° = 300°
2x + 30° = -60°
2x + 30° = -300°
Subtracting 30° to all the equations:
2x = 60° - 30° = 30°
2x = 300° - 30° = 270°
2x = -60° - 30° = -90°
2x = -60° - 300° = -360°
Dividing by 2 we have the complete set of solutions:
x = 15°
x = 135°
x = -45°
x = -180°
