Write an expression that generates all angles coterminal with each angle. Let n represent any integer. 135°

Verified step by step guidance

1. Understand that coterminal angles are angles that share the same terminal side when drawn in standard position.
2. To find coterminal angles, you can add or subtract full rotations (360°) to the given angle.
3. Express the general formula for coterminal angles as: \( \theta + 360n \), where \( \theta \) is the given angle and \( n \) is any integer.
4. Substitute the given angle (135°) into the formula: \( 135° + 360n \).
5. This expression \( 135° + 360n \) will generate all angles coterminal with 135° for any integer \( n \).

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find coterminal angles, you can add or subtract multiples of 360° (for degrees) or 2π (for radians) to the given angle. For example, 135° and 495° are coterminal because 495° = 135° + 360°.

Integer Representation

In the context of generating coterminal angles, 'n' represents any integer, which allows for the creation of an infinite set of angles. By substituting different integer values into the expression for coterminal angles, you can generate all possible angles that are coterminal with the original angle. This flexibility is crucial for understanding the periodic nature of trigonometric functions.

Angle Measurement

Angles can be measured in degrees or radians, and understanding this distinction is essential when working with trigonometric concepts. In this case, the angle is given in degrees (135°), and when generating coterminal angles, it is important to consistently use the same unit of measurement. Converting between degrees and radians may be necessary depending on the context of the problem.