1. Lesson 1

1.4. Discover

Mathematics 30-2 Module 6

Module 6: Sinusoidal Functions

 

Discover

 

In Try This 1 you will investigate the relationship between the radius and circumference of a circle.

 

Try This 1

 

Complete either Investigation A or Investigation B. You will need a protractor and a pipe cleaner or a string to complete Investigation A. Investigation B does not require any materials.

 

Investigation A



textbook

Complete questions A, B, C, D, E, and F on page 484 of your textbook.

 

Investigation B

 

Open Radian Explorer.

 

 

This is a play button for Radian Explorer.

 

Under “Circle Size,” select “Large.”

 

Step 1: Click on the red line under “Radius” and drag the line toward the circle.

 

Step 2: Click the “bend” toggle at the end of the new radius. The new line is the same length as the radius but now matches the curve of the circle.

 

Step 3: Place the curved radius on the circle so one end touches the original black radius.

 

Step 4: Make and curve a few radii. In order to do this, click on “Radius” and drag the line to the circle. You can curve the radius by clicking on the end of the red line (see step 2). Place radii on the circumference of the circle from end to end. Determine how many radii are needed to go around the entire circle. Record this number.

 

Step 5: Select the “Angle Guide Controls” and rotate the guide so that it touches the other end of one curved radius, as in the following diagram.

 

This diagram shows a central angle subtended by an arc of length one radius.

 

Step 6: Use the protractor to measure the acute angle at the centre of the circle. Record the size of this angle.

 

Repeat steps 1 to 6 using the “Small” and “Medium” circle sizes. Then answer the following questions.

  1.  Describe how many radii are needed to go around each circle.
    1. large circle
    2. small circle
    3. medium circle
  2. How did the circle size affect the number of radii needed?
  3. Describe how large the angle you measured in step 6 was for each of the circles.
    1. large circle
    2. small circle
    3. medium circle
  4. How did the circle size affect the angle size?

course folder Save your responses in your course folder.

 

Share 1

 

With a partner or in a group, discuss the following questions based on the information from Try This 1.

  1. What is the physical relationship between the circumference of a circle and the length of its radius that you found in Try This 1? How does this relate to C = 2πr or
  2. In both activities you were to measure the angle made by the arc length, r. (See the following image.) This angle is equal to 1 radian measure. Estimate how many degrees would be equal to 2π radians.

    This diagram shows a central angle subtended by an arc of length one radius. The angle is labelled 1 radian.

course folder If required, save a record of your discussion in your course folder.