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

In article <MuSdneADj_a25MbanZ2dnUVZ_tajnZ2d@[EMAIL PROTECTED]
>,
Darrell wrote:

> Daniel C. Bastos wrote:
>> In article <mYednSPOcuujw8banZ2dnUVZ_urinZ2d@[EMAIL PROTECTED]
>,
>> Darrell wrote:
>> 
>>> Daniel C. Bastos wrote:
>>>
>>>>> 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?
>>>> Both equivalent to zero.
>>> In the same spirit, would you say any two graphs of a unit circle have

>>> equivelent paremetric equations?
>> 
>> Hm, I think so. If they represent the same graph, they must satisfy the
>> same pairs (x, y). So they must be equivalent.
>
> Consider these two (different) pairs of parametric equations.
>
> a) x = t
>     y = 3t - 2
>
>
> b) x = t - 3
>     y = 3t - 11
>
> Find their rectangular equations:
>
> a) y = 3x - 2   ...simple substitution

Okay.

>
> b) 3(x = t - 3)
>     -(y = 3t - 11)
>
> add:
>     3x =  3t - 9
>     -y = -3t + 11
>   -----------------
>   3x-y =        2
>     -y = -3x + 2
>      y =  3x - 2

Okay. I was having trouble with your notation, so I wrote x + 3 = t and
then y = 3(x + 3) - 11 = 3x + 9 - 11 = 3x - 2. So these two are
equivalent. They must also have the same graph. I still follow you.