Help with reparameterizing

[brandtw]

I think that i'm just having problems with my derivitives and integrals. If someone one could show me what the steps of this problem look like it would be greatly appreciated. "Reparameterize the curve with respect to the arc length measured from the point where t=0 in the direction of increasing t. r(t)=e^t*sint i +e^t*cost j"

[HallsofIvy]

Looks like homework to me!

Step 1: If you want to use arc-length as a parameter, then you will need to know what the arc-length is! The formula for arclength, given x and y in terms of parameter t, taking t= 0 as starting point and t>0 as positive arclength, is:
s(t)= \int_0^t\sqrt{x'^2+y'^2}dt.

Step 2: That will give you arclength, s, as a function of t. Now solve for t as a function of s and substitute that formula into your parametric equations.