- #1
motornoob101
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Homework Statement
Find the place where the parametric curve intersect itself
[tex] x = 1-2cos^{2}t [/tex]
[tex] y = tant(1-2cos^{2}t)[/tex]
Homework Equations
The Attempt at a Solution
So I started with the x values..
[tex] 1-2cos^{2}t_{1} = 1-2cos^{2}t_{2} [/tex]
By canceling the same stuff on both sides, I got
[tex] cos^{2}t_{1} = cos^{2}t_{2} [/tex]
Then I tried with y
I rewrote y in a different form.
[tex] y_{1} = tan t (x_{1}) [/tex]
and
[tex]y_{2} = tan t(x_{2}) [/tex]
This is possible since y already contains an expression for x.
Since the curve intersect itself, we know x1 must equal x2 so they cancel out.
then I am left with [tex] tant_{1}= tant_{2} [/tex]
but I can't solve for t
Appreciate any help. Thanks