1. Lesson 1

1.9. Explore 5

Mathematics 30-2 Module 6

Module 6: Sinusoidal Functions

 

So far, you have looked at angles between 0° and 360° or 0 and 2π. It is also possible to express angles larger than 360°. Open Angles Larger than 360° and move the angle slider to see a representation of larger angles.

 

 

This is a play button that opens Angles Larger than 360°.

 

Angles Larger than 360° can be used to describe objects that rotate. A spiral is often used to show this in a diagram.

 

This diagram shows an angle larger than 360° represented with a spiral.

This is an angle larger than 360°.

 

In Try This 4 you will explore the rotation of the minute hand on a clock.

 

Try This 4

 

This graphic shows a clock with both the minute hand and hour hand pointed towards the 12.

iStockphoto/Thinkstock

  1. Suppose it is 12:00 right now. Explain how many degrees the minute hand has travelled when it is
    1. 12:15, fifteen minutes later
    2. 1:15, an hour and fifteen minutes later
    3. 1:40, an hour and forty minutes later
  2. Suppose it is 12:00 right now. Explain what time will it be when the minute hand has travelled
    1. 210°
    2. 510°
    3. 5π rad
  3. Describe a procedure that will determine the time, given an angle in degrees, through which the minute hand has moved in a clockwise direction.

course folder Save your responses in your course folder.

The minute hand travels 360° in 60 min, or 6° per minute.
The minute hand travels 360° in 60 min, or 6° per minute.