Problem 104 - Algebra and Trigonometry

Question

Explain the difference between positive and negative angles. What are coterminal angles?

Step-by-Step Solution

Answer

Positive angles are measured counterclockwise from the positive x-axis, while negative angles are measured clockwise. Coterminal angles are those which, in a standard coordinate system, share the same initial and terminal sides.

Step 1: Explaining Positive and Negative Angles

Angles in a coordinate system are considered positive if they are measured counterclockwise from the positive x-axis, and negative if they are measured clockwise. An angle of \(0^\circ\) is neither negative nor positive and is typically measured along the positive x-axis.

Step 2: Understanding Coterminal Angles

Coterminal angles are angles in a standard coordinate system that share the same initial and terminal sides. They are named so because they 'terminate' or end at the same position. For instance, the angles \(30^\circ\) and \(390^\circ\) are coterminal, because if you start at the positive x-axis and rotate \(30^\circ\) counterclockwise, you’ll end up at the same spot as if you rotate \(390^\circ\) counterclockwise. Mathematically, two angles are coterminal if they differ by an integer multiple of \(360^\circ\).