Here is what I wrote:
"Sine is an odd function because whenever it passes under the x-axis, it becomes negative.
A 3-4-5 (point (3,4) on a circle) triangle in the first quadrant would have a sine value of sin(4/5). If the triangle were reflected over the x-axis, the sine value would change to sin(-4/5).
Another rationale why sine is negative is because it has no symmetry over the x or y axis. Cosine is symmetric over the y-axis, thus it is even. "
I'm not sure if this is answering the question, or if it is too "far out..." ???