What are coterminal angles?

Coterminal angles are angles that share the same terminal side when drawn in standard position, even if they have different measures. This means that when you rotate an angle, you can end up at the same position after completing full rotations.

Understanding Coterminal Angles

To find coterminal angles, you can add or subtract full rotations, which are multiples of 360 degrees (for degrees) or 2π radians (for radians).

Examples of Coterminal Angles

• For Degrees: 30° and 390° are coterminal because 390° - 360° = 30°.
• For Radians: π/4 and 9π/4 are coterminal since 9π/4 - 2π = π/4.

Finding Coterminal Angles

To calculate a coterminal angle, use the formula:

Coterminal Angle = Original Angle ± 360n

Here, n is any integer (positive or negative). This allows you to find an infinite number of coterminal angles.

Why They Matter

Coterminal angles are useful in trigonometry, as they help simplify problems involving angle measures and can make calculations easier by reducing angles to a standard range.