# 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()