Curve problem

1. Feb 11, 2008

rcmango

1. The problem statement, all variables and given/known data

Prove that the curve x = t cos(t), y = (pi/2 - t) sin(t) has a self-intersection at the point (0,0)

2. Relevant equations

3. The attempt at a solution

2. Feb 11, 2008

jhicks

Find two t's such that x(t1)=y(t1)=x(t2)=y(t2)=0. Both x(t) and y(t) take periodic visits to 0, so it shouldn't be too hard to find. The construction of x(t) and y(t) give clues as to which values are good to look at first.

3. Feb 11, 2008

rcmango

Okay, so if i'm looking for two t's that both are 0 at x and y, i should be looking at the sin and cos graph where both are 0, correct?

so one good point would be (x1, y1) are 0,0 itself.
and the other point is about 1.571, where both graphs touch this point at the x axis.

are these points okay?

okay whats next!

4. Feb 11, 2008

Dick

So what values of t are you talking about?

5. Feb 11, 2008

rcmango

0 and 1.571

unless there is something easier you can suggest other than 1.571

6. Feb 12, 2008

Dick

That will do it. I kinda like pi/2 better than 1.571 though. And since cos(t) and sin(t) are never zero at the same value of t, they are the only two.

Last edited: Feb 12, 2008