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 angles are coterminal if they differ by full rotations of 360°. This means adding or subtracting multiples of 360° to the given angle will produce all coterminal angles.
2. Identify the given angle, which is 135° in this problem.
3. Express the general form of all coterminal angles by adding 360° multiplied by an integer \( n \), where \( n \) can be any integer (positive, negative, or zero).
4. Write the expression for all coterminal angles as \( 135° + 360° \times n \).
5. Note that \( n \in \mathbb{Z} \) (the set of all integers), which ensures you cover every possible coterminal angle.

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations. They can be found by adding or subtracting multiples of 360° to the given angle, resulting in angles that have the same terminal side position.

General Formula for Coterminal Angles

The general expression for all angles coterminal with a given angle θ is θ + 360°n, where n is any integer. This formula accounts for all possible rotations around the circle, both clockwise and counterclockwise.

Integer Parameter n

The variable n represents any integer (positive, negative, or zero) and indicates the number of full 360° rotations added or subtracted. This allows the formula to generate infinitely many coterminal angles by varying n.