Curve problem

[TheAngryMathStudent]

Long story short, had assignment which I had to re-do over easter, but because I
had pre-ordered tickets I'm only going back tonight and the 2nd attempt is due
tomorrow. Since I don't have access to anyone else, I turn to you guys. I
thought I'd make it by now, but I'm not gonna work it out on my
own.


A curve is given by

x(t) = 3(t - sin(t))
y(t) = 3(1- cos(t))

Find the parameterized "normalcurve" x(s;t); y(s;t) that
goes through (x(t); y(t)) where s is the parameter to
"normalcurve"

(I don't know the English Word for it, but
normalcurve is the 90 degree angle of a line, I'm not quite sure how to
formulate it?)

I've drawn up the curve. I figured if I managed to
calculate the curve that's opposite (lowpoint where the other one has highpoint)
then that curve would
it? Kinda like a wildshot too be quite honest.

 

[HallsofIvy]

So, you want to find parametric equations, with parameter s, for the curve that is perpendicular to x= 1- sin(t), y= 1- cos(t), at each value of t?

Okay, "normal" or "perpendicular" means that the slope is -1/m where m is the slope of the given curve. Do you know what the slope of the given curve, at a specific value of t, is?

Actually, it might be simpler to use the "peculiar" properties of this particular curve and not use differential equations at all. What kind of curve is it?
(notice that 1- x= sin(t) and 1- y= cos(t).)

 

[Deleted member 4993]

So, you want to find parametric equations, with parameter s, for the curve that is perpendicular to x= 1- sin(t), y= 1- cos(t), at each value of t?

Okay, "normal" or "perpendicular" means that the slope is -1/m where m is the slope of the given curve. Do you know what the slope of the given curve, at a specific value of t, is?

Actually, it might be simpler to use the "peculiar" properties of this particular curve and not use differential equations at all. What kind of curve is it?
(notice that 1- x= sin(t) and 1- y= cos(t).)

The original curves are different from the one you wrote:

original curves:

x(t) = 3[t - sin(t)]
y(t) = 3[1- cos(t)]