If θ is defined as the rotation in degrees CCW ( counter clockwise) and the starting point [0.0°] is the "x" axis to the right positive = cos, and the "y" axis up as positive = sin. Initially cos(θ) is 1.0 [length] when angle θ is 0.0°. So ∫ sin(θ)["y"] δθ = -cos(θ) ["x"] is cyclic in a certain direction defined by convention and I am cool with that as long as it is realized that it is purely something that is constructed to deal with specific issues in a mathematical and logical way. This is one of those places where I question the way in which things are integrated in the same way as ∑m•v δv. It is valid in context and provable, however, is it indicative of some vast absolute universal truth? I suspect not.
Wikipedia has a good page for trigonometric functions as they are defined.
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