Math Example--Angle Concepts--Angle Measures: Example 27

Topic

Geometry

Description

This example presents a negative angle of -45 degrees on a polar coordinate graph. The angle is marked in red and located in the fourth quadrant. Students are asked to identify the angle shown, with the solution explaining that the absolute value of the angle (45°) makes it an acute angle, and it is coterminus with 315° (calculated as 360° - 45°).

As part of a series on angle measures, this example helps reinforce the understanding of negative and coterminus angles. By using a polar coordinate system, students can visualize how angles in the negative direction relate to their positive counterparts on the graph.

Repeated exposure to various negative angles helps solidify the concept and allows students to quickly identify angle types. This repetition is essential for establishing a solid foundation in geometry.

Teacher Script: "Let's examine this -45-degree angle, class. What does the negative sign indicate about the direction of rotation? Can you explain why the absolute value classifies it as acute? Lastly, let's discuss its coterminus angle of 315°. How important do you think understanding negative and coterminus angles is in real-world scenarios?"

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