Give two positive and two negative angles that are coterminal with the given quadrantal angle. 270°

Verified step by step guidance

1. Understand that coterminal angles differ by full rotations of 360°. This means if you add or subtract multiples of 360° to the given angle, you get coterminal angles.
2. Start with the given angle, which is 270°, a quadrantal angle lying on the negative y-axis.
3. To find two positive coterminal angles, add 360° and 720° to 270° respectively, using the formula \(\theta + 360^\circ \times n\) where \(n\) is a positive integer.
4. To find two negative coterminal angles, subtract 360° and 720° from 270° respectively, using the formula \(\theta - 360^\circ \times n\) where \(n\) is a positive integer.
5. List the resulting angles as your two positive and two negative coterminal angles with 270°.

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 360°. To find coterminal angles, you add or subtract multiples of 360° from the given angle. This concept helps identify angles that have the same trigonometric values.

Quadrantal Angles

Quadrantal angles are angles whose terminal sides lie along the x-axis or y-axis, typically at 0°, 90°, 180°, 270°, or 360°. These angles are important because their trigonometric values are often simple or undefined, and they serve as reference points in the coordinate plane.

Positive and Negative Angles

Positive angles are measured counterclockwise from the positive x-axis, while negative angles are measured clockwise. Understanding this distinction is essential when finding coterminal angles, as you can add or subtract 360° to generate both positive and negative coterminal angles.