Give two positive and two negative angles that are coterminal with the given quadrantal angle. 90°

Verified step by step guidance

1. Understand that coterminal angles are angles that share the same terminal side when drawn in standard position.
2. To find coterminal angles, add or subtract multiples of 360° to the given angle.
3. For positive coterminal angles, add 360° to 90° to get the first positive coterminal angle, and then add another 360° to get the second positive coterminal angle.
4. For negative coterminal angles, subtract 360° from 90° to get the first negative coterminal angle, and then subtract another 360° to get the second negative coterminal angle.
5. Verify that all calculated angles are indeed coterminal by checking that they differ from 90° by a multiple of 360°.

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find coterminal angles, you can add or subtract multiples of 360° (for degrees) or 2π (for radians) from the given angle. For example, if you start with 90°, adding 360° gives you 450°, while subtracting 360° results in -270°.

Quadrantal Angles

Quadrantal angles are angles that are located on the axes of the coordinate plane, specifically at 0°, 90°, 180°, and 270° (or their equivalents in radians). These angles are significant in trigonometry because their sine and cosine values are well-defined and can be easily calculated. The angle 90° is a quadrantal angle, making it a key reference point for determining coterminal angles.

Positive and Negative Angles

Positive angles are measured counterclockwise from the positive x-axis, while negative angles are measured clockwise. In the context of coterminal angles, both positive and negative angles can be derived from a given angle by adding or subtracting full rotations (360°). This concept is essential for understanding how angles can be represented in different ways while still pointing in the same direction.