Lesson 2: Applications of Radians

Focus

The Reichstag dome is a glass dome built on top of the Reichstag building in Berlin, Germany. Inside the Reichstag dome are circular paths.

If you walked around one of these circular paths once, could you determine how far you had walked? How about three times? What would be different if you only hiked part of the circle? In each scenario, what would you need to know in order to determine how far you had walked?

In this lesson you will expand your knowledge of degrees and radians and determine how these units can be used in real-life situations.

Lesson Outcomes

At the end of this lesson you will be able to

• determine angles that are coterminal with a given angle
  
• determine the general form of all angles that are coterminal with a given angle
  
• explain the relationship between arc lengths, central angles, and the radius of a circle and solve problems using this relationship

Lesson Questions

You will investigate the following questions:

• How can angles with the same terminal arms be described?
  
• How can the relationship between the central angle, arc length, and radius in a circle be used to solve real-life problems?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 2 Assignment (Download the Lesson 2 Assignment and save it in your course folder now.)
• course folder submissions from Try This and Share activities
• additions to Glossary Terms and Formula Sheet
• work under Project Connection