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.
  1. Check "Radians" to view t as a decimal number.
  2. Move t to integer values such as 1, 2, 3, -1, etc. and answer the following questions:
    1. Which integer wraps closest to halfway around the circle?
    2. Which integer wraps closest to one time around the circle?
    3. Which integer wraps closest to twice around the circle? (Note that you have to zoom out to get t large enough)
  3. Check "Multiples of π" to view t as rational multiples of π.
    1. Which multiples of π wrap to the top of the circle, (0,1)? (You should be able to find both positive and negative answers.)
    2. Which multiples of π wrap to the left of the circle, (-1,0)?
  4. Check "Degrees" to view t in degrees.