This isn't really a HW question, it's just something that's been confusing me in my Calc class. We recently went over how to find curvatures of curves in 3D space. In lecture, the professor went over a simple example: a circle of radius 3 at any given point. Maybe it's because I don't remember my Calc II class that well, but he parameterized the equation of a circle, x2 + y2 = 9 to become r(t) = 3cos(t)i + 3sin(t)j . So from: x2 + y2 = r2 If x = cos(t) and y = sin(t), the identity cos2(t) + sin2(t) = 1 still holds true. If the radius is 3, x2 + y2 = 32 3(x2 + y2) = 9(12) 9cos2(t) + 9sin2(t) = 9(12) 9(cos2(t) + sin2(t)) = 9(12) is how I understand it. If there's an easier way to picture it, please let me know! So then r(t) = 3cos(t)i + 3sin(t)j describes the circle when "traced." My question: why does the "x" part and the "y" part of the parameterization have to be the respective cos, sin trig functions? In class, one student said that x was sin; but the prof said that no, it's cos. Why does x have to be cos, rather than sin? Does it have to do something with the direction the curve "goes in?" How can I determine the "direction" the curve goes in? Or did I just hear my professor wrong...?