Write an expression that generates all angles coterminal with each angle. Let n represent any integer. ―90°

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Understand that coterminal angles are angles that differ by full rotations. Since one full rotation is 360°, coterminal angles can be found by adding or subtracting multiples of 360°.

Let the given angle be \(-90^\circ\). To find all angles coterminal with \(-90^\circ\), add \(360^\circ\) multiplied by any integer \(n\) to the angle.

Write the general expression for coterminal angles as: \(-90^\circ + 360^\circ \times n\) where \(n\) is any integer (\(n \in \mathbb{Z}\)).

This expression generates all angles that share the same terminal side as \(-90^\circ\) when drawn in standard position.

Remember that \(n\) can be positive, negative, or zero, which accounts for rotations in both directions and the original angle itself.

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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° (for degrees) or 2π (for radians) to the given angle.

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 rotations added or subtracted. This allows the formula to generate infinitely many coterminal angles by varying n.