Different ways can be used to determine the distance the horse travelled in Try This 3. You may have seen that if you know what proportion of the circle was travelled and the circumference of the circle, you can calculate the distance travelled by the horse. A completed portion of the table from Try This 3 shows example calculations that could be used to find the distance and angle travelled.
| 4 s | |
| Fraction of 1 Revolution |  of a revolution |
| Distance Travelled by White Horse to the Nearest Tenth of a Metre, or Arc Length | circumference × amount of a revolution
|
| Diagram of Rotational Angle in Standard Position |  |
| Angle of Rotation in Degrees |  |
| Angle of Rotation in Radians |  |
In Try This 4 you will see another way to look at the arc length around a circle. You will look at the relationship between arc length, radius, and central angle.
Try This 4
Step 1: Open Unwrapping a Circle and click on Show radius scale and Show radian measure.
Step 2: Change each arc length to match the value in the table that follows. Use your keyboard’s arrow keys to move the slider in smaller increments.
Step 3: Slide the Unwrap slider to the right to see the arc length of the circle stretched out, and then measure the length by the number of radii using the radius scale.
Complete a table like the one shown.
| Arc Length | Radian Measure of Angle (α) | Radius Scale |
| 2 | 1 | 1 r (radius) |
| 4 | ||
| 8 | ||
| 3.14 | ||
| 6.28 |
Save a copy of your table in your course folder.
Share 3
Discuss your responses with a classmate. In your discussion, address the following points.
- Based on the patterns you see in the table, how could you find the arc length if given the radian measure of the angle and the radius of the circle?
- What is the relationship between arc length, radius, and radian measure?
If required, save a record of your discussion in your course folder.