# Wrapping Function

- Author:
- Ron Smith

Move

*t*on line*L*to see the wrapping function*W(t)*. Each real number*t*on line*L*corresponds to a point*W(t)*on the unit circle*C*. The point is found by wrapping*L*about*C*without slipping or stretching. The coordinates of*W(t)*are (cos*(t)*, sin*(t)*). This is the definition of cosine and sine.- Check "Radians" to view t as a decimal number.
- Move t to integer values such as 1, 2, 3, -1, etc. and answer the following questions:
- Which integer wraps closest to halfway around the circle?
- Which integer wraps closest to one time around the circle?
- Which integer wraps closest to twice around the circle? (Note that you have to zoom out to get t large enough)

- Check "Multiples of π" to view t as rational multiples of π.
- Which multiples of π wrap to the top of the circle, (0,1)? (You should be able to find both positive and negative answers.)
- Which multiples of π wrap to the left of the circle, (-1,0)?

- Check "Degrees" to view t in degrees.