# Wrapping a Line Around a Circle

- Author:
- L. Marizza A. Bailey, Ron Smith

- 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 .

**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()?

## Cosine of an angle

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

## Review of Radians

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

## 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()