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

Verified step by step guidance

1. 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°.
2. 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.
3. Write the general expression for coterminal angles as: \(-90^\circ + 360^\circ \times n\) where \(n\) is any integer (\(n \in \mathbb{Z}\)).
4. This expression generates all angles that share the same terminal side as \(-90^\circ\) when drawn in standard position.
5. Remember that \(n\) can be positive, negative, or zero, which accounts for rotations in both directions and the original angle itself.

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° (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.