Question

Solve cos(2x + 30) = 0.5 for -180≤x≤180​

Answer 1

Answer:

x = 15°

x = 135°

x = -45°

x = -180°

Step-by-step explanation:

Trigonometric Equations

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°