Wrapping Function
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.