# Wrapping a Line Around a Circle

Topic:
Circle
THE UNIT CIRCLE: C is the circle of radius =1, centered at the origin. 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. Find the x and y coordinates for the given degree values of t, listed below. Make a table and create a column with the x and y coordinates in ordered pair form:
 ﻿a. t = 0﻿o ﻿b. t = 30﻿o ﻿c. t = 45﻿o ﻿d. t = 60﻿o ﻿e. t = 90﻿o ﻿f ﻿ t= 180o ﻿
 ﻿g. t = 270o﻿ ﻿ ﻿h. t = 360﻿o ﻿ ﻿i. t = 450﻿o ﻿ ﻿j. t = -60﻿o ﻿ ﻿k t = -90﻿o ﻿ l.﻿ ﻿t = -180o ﻿