Re: parametric: x = cos(t), y = sin(t)

Daniel C. Bastos wrote:

<...>

> But I'm not actually trying to avoid geometry per se; I'm trying to
> avoid geometric pictures.

That's akin to saying I'm not trying to avoid a plane curve, just trying 
to avoid its graph.

But a plane curve is a set of parametric equations _and_ a graph.

> I like algebra theorems, in which from an
> equation we derive another without any external help. I like this
> because it is safe; it depends very little on human interpretation,
> unlike pictures.

I would argue it depends highly on human interpretation.


<...>

> So it seems to me that the problem is whether we should let the word
> ``angle'' stand for measures between 0 and 180 or any number? I would be
> happy with a definition that states that angles are equivalence cl*****
> with the angles whose measures lie in [0,360) being the representatives
> of the cl***** --- if this can be done as my intuition says so.

Don't confuse "angle" with a measure.  An angle is a mathematical 
object.  Its measure is another thing entirely.

Going back to an angle in standard position, as previously explained, 
would you say an angle of 360deg is equivalent to and angle of 0?  Or to 
an angle of -360deg?

-- 
Darrell