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

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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.

Identify the given angle, which is 135° in this problem.

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).

Write the expression for all coterminal angles as \( 135° + 360° \times n \).

Note that \( n \in \mathbb{Z} \) (the set of all integers), which ensures you cover every possible coterminal angle.

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주요 개념

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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.