(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The parametric function :

x = cos(5t)

y= cos(3t)

t belongs to R

Question : find the coordinates (x, y) of the double points

2. Relevant equations

3. The attempt at a solution

OK so first of all,i find an interval of t where to study

- periodic of 2Pi

- M(t) = M(-t)

- M(t+Pi) is the symmetric of M(t) by point O

- M(Pi-t) is the symmetric of M(t) by point O

So i decide to study on E=[0, Pi/2], and then just do the symmetric by O to get it on [0, Pi]

and since M(t) = M(-t), then i have it on [-Pi, Pi], which is an interval of 2Pi, meaning that i have it on R.

here is a graph

Now i need to get the coordinates (x, y), of the 4 "double points"

knowing that there is a symmetry by O, i just need to find the coordinates of 2 non-symmetric of the 4.

but now i am stuck, because we have just spent one class all this, what is the method to find these double points ?

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Logically, if 'u' belongs to E=[0, Pi/2] and 'w' belongs to F=[Pi/2, Pi],

we are looking for x(u) = x(w) AND y(u) = y(w)

but i was thinking we might need to use the symmetry too

so, we consider 'z' belongs to E=[0, Pi/2], with

x(w) = - x(z)

y(w) = - y (z)

I have tried with this, but doesn't give me any concluding results, since it just expresses me w with z :D

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# Homework Help: Parametric function - double points

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