Wrapping a Line Around a Circle

Topic:
Circle

THE UNIT CIRCLE

The unit circle is a circle, C, of radius 1, centered at the origin (0,0). As we move up line L, we are going to imagine wrapping the line around C. The value of t becomes the length of the arc which has been wrapped around C. Since this is a circle of radius 1
  • wrapping around the whole circle () would require a length of .
  • wrapping around half the circle () would require a length of .
You can zoom in and out to see higher values of arc length and degrees. Every point on the line L corresponds to a point on the circle. This is called the wrapping function.

Investigations of the Wrapping Function

1. Click on the degrees, and click off the Arc Length and Right Triangle.

2. Move the point t up and down the line. Observe the x and y coordinates. 3. Click on right triangle and click off arc length and degrees. 4. Use the right triangle to find the sin(), cos( where is the angle from the positive x axis to the point on the unit circle (not the angle in green. How are the sine and cosine related to the x and y coordinates?

Sine of an angle

Which of the following is equivalent to the sin()?

Check all that apply

Cosine of an angle

Which of the following is equivalent to the cos()?

Check all that apply

Review of Radians

Which of the following is the DEFINITION of the angle measure in radians.

Check all that apply

Use the Unit Circle above to find the sin(90)

Use the Unit Circle above to find the radian measure of .

Use the Unit Circle above to find cos()