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

Given that the tangent to the curve [itex] c(t) [/itex] at any point on the curve is [itex] T(t) = (-sin(t), cos(t) )[/itex], find [itex] c(t) [/itex] if the curve passes through the point [itex] (0,0) [/itex].

3. The attempt at a solution

I try to let

[itex] c(t) = ( x(t), y(t) ) [/itex]

Then

[itex] c'(t) = ( x'(t), y'(t) ) [/itex]

[itex]| c'(t) | = \sqrt{[x'(t)]^2 + [y'(t)]^2 } [/itex]

And

[itex] T(t) = \frac{c'(t)}{|c'(t)|} [/itex]

However this is complicated and consequently I am not sure how to solve it. I am also not sure how to "use" the point given since (0, 0) correspond the the values x and y respectively rather than t.

Thanks.

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# Homework Help: Find the curve given the tangent

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