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})
```