Math Example--Angle Concepts--Angle Measures: Example 25

Topic

Geometry

Description

This example features a negative angle of -15 degrees on a polar coordinate system. The angle is drawn in red, and the grid includes angles labeled from 0° to -360° in increments of 15° and 30°. Students are asked to identify the angle shown, with the solution explaining two key points: the absolute value of the angle (15°) makes it an acute angle, and it is coterminus with 345° (calculated as 360° - 15°).

As part of a series on angle measures, this example introduces the concept of negative angles and coterminus angles. By using a polar coordinate system, students can visualize how negative angles relate to positive angles and understand their significance in geometry and trigonometry.

This example helps students develop a more comprehensive understanding of angle measures, extending beyond the basic positive angle concepts. It reinforces the idea that angles can be represented in multiple ways, which is crucial for advanced mathematical thinking.

Teacher Script: "Let's examine this -15-degree angle, class. What does the negative sign tell us about the direction of rotation? Can someone explain why we consider its absolute value when classifying it as acute? Now, let's discuss what it means for this angle to be coterminus with 345°. How might understanding negative and coterminus angles be useful in real-world applications?"

For a complete collection of math examples related to Angle Measures click on this link: Math Examples: Angle Measures Collection.