Move [i]t[/i] on line [i]L[/i] to see the wrapping function [i]W(t)[/i]. Each real number [i]t[/i] on line [i]L[/i] corresponds to a point [i]W(t)[/i] on the unit circle [i]C[/i]. The point is found by wrapping [i]L[/i] about [i]C[/i] without slipping or stretching. The coordinates of [i]W(t)[/i] are (cos[i](t)[/i], sin[i](t)[/i]). This is the definition of cosine and sine.
[list=1] [*]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: [list=a] [*]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) [/list] [*]Check "Multiples of π" to view t as rational multiples of π. [list=a] [*]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)? [/list] [*]Check "Degrees" to view t in degrees. [/list]