Math Example--Angle Concepts--Angle Measures: Example 29

Topic

Geometry

Description

This example presents a negative angle of -75 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 (75°) makes it an acute angle, and it is coterminus with 285° (calculated as 360° - 75°).

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

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

Teacher Script: "Let's examine this -75-degree angle, class. What does the negative sign indicate about the direction of rotation? Can you explain why the absolute value still classifies it as acute? Lastly, let's discuss its coterminus angle of 285°. How important do you think understanding negative angles and their coterminus positive angles is in fields like physics or engineering?"

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