Lesson 1: Radians and Degrees in Standard Position

 

Focus

 

When asked to measure angles in circles or triangles in previous math courses, you likely gave your response using the unit of degrees. Why degrees? Did you know that there are other units you can use to measure angles? Why not use radians, gradients, or arc minutes?

 

Do you know why there are 360° in a circle? One theory gives credit to the ancient Babylonians. The ancient Babylonians, who lived from approximately 2000 BC, used a sexagesimal (base-60) number system instead of the base-10 number system used today.

Another theory is that the ancient Babylonians believed the sun revolved around Earth in approximately 360 days, and that there were 60 days in each season. Or maybe 360 was chosen because it is so easily divided by 24 numbers.

 

In this lesson you will learn about measuring angles in a unit other than degrees.

 

Lesson Outcomes

 

At the end of this lesson you will be able to

• define radian measure
• determine a relationship between degrees and radians
• determine a method for converting between degrees and radians and between radians and degrees
• sketch angles given in degrees and radians, positive and negative, in standard position

Lesson Questions

 

You will investigate the following question:

• What relationship exists between degree and radian measures?

Assessment

 

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

• completion of the Lesson 1 Assignment (Download the Lesson 1 Assignment and save it in your course folder now.)
  
• course folder submissions from Try This and Share activities
  
• additions to Glossary Terms
  
• work under Project Connection

Self-Check activities are for your own use. You can compare your answers to suggested answers to see if you are on track. If you have difficulty with concepts or calculations, contact your teacher.

 

Remember that the questions and activities you will encounter provide you with the practice and feedback you need to successfully complete this course. You should complete all questions and place your responses in your course folder. Your teacher may wish to view your work to check on your progress and to see if you need help.

 

Time

 

Each lesson in Mathematics 30-1 Learn EveryWare is designed to be completed in approximately two hours. You may find that you require more or less time to complete individual lessons. It is important that you progress at your own pace, based on your individual learning requirements.

 

This time estimation does not include time required to complete Going Beyond activities or the Module Project.