My Math Forum Any special case satisfying $\arctan{\frac{dy(c+s)} {dx(c+s)}}$

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 January 20th, 2015, 07:25 PM #1 Newbie   Joined: Oct 2014 From: China Posts: 12 Thanks: 2 Any special case satisfying $\arctan{\frac{dy(c+s)} {dx(c+s)}}$ There is a mysterious parametric curve: $$x(s),y(s)$$ defined on three intervals (continuity unkown) around a, b, and c $(a< b\leq c)$, thus the curve consists of three segments : $$x(a+s) ,y(a+s)$$ $$x(b-s) ,y(b-s)$$ $$x(c+s) ,y(c+s)$$ that satisfy the following equations: $$\frac{dy(c+s)}{dx(c+s)}=\frac{y(c+s)-y(b-s)}{x(c+s)-x(b-s)}$$ $$\frac{dy(a+s)}{dx(a+s)}=\frac{y(a+s)-y(b-s)}{x(a+s)-x(b-s)}$$ $$\arctan{\frac{dy(c+s)} {dx(c+s)}}-\arctan{\frac{dy(a+s)} {dx(a+s)}}=\pi-\theta$$ here: $$\frac{dy(c+s)/ds}{dx(c+s)/ds}=\frac{dy(c+s)}{dx(c+s)}$$ I guess the conditions above are not sufficient to work out $x(s), y(s)$ , however, is it possible to give any special case satisfying above equations? Now I have no clue how to go any further on this problem.Thanks for any suggestions.
 January 21st, 2015, 06:37 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 What do you mean by "dy(c+s)"?
January 21st, 2015, 06:01 PM   #3
Newbie

Joined: Oct 2014
From: China

Posts: 12
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Quote:
 Originally Posted by Country Boy What do you mean by "dy(c+s)"?
dy(c+s) means d(y(c+s)) the infinitesimal change in y(as a function of s), c is a constant.

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