# calculus and analysis – Findroot and arc length,similar situation but does not work

In another problem I was presented with this situation
It is to find the arc length of the curve

``````  x = 50 (1 - Cos(t)) + 50 (2 - t) Sin(t);
y = 50 Sin(t) + 50 (2 - t) Sin(t);
``````

from t=0 to t =tmax , in such a way that the length is 100 units

which works perfectly

``````FindRoot(ArcLength({x, y}, {t, 0, tmax}) == 100, {tmax, 1})
{tmax -> 0.832919}
``````

, then an error was discovered in the second equation and I tried to do the same but it does not work.

``````  x = 50 (1 - Cos(t)) + 50 (2 - t) Sin(t);
y = 50 Sin(t) + 50 (2 - t) Cos(t);
FindRoot(ArcLength({x, y}, {t, 0, tmax}) == 100, {tmax, 1})

(*FindRoot::nlnum: The function value {False} is not a list of numbers with dimensions {1} at {tmax} = {1.}.*)
``````

I changed it to 2 because at t=2 100 units are produced but it does not work. I don’t understand why

``````FindRoot(ArcLength({x, y}, {t, 0, tmax}) == 100, {tmax, 2})
``````

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