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## Homework Statement

Find a tangent vector

**r**that satisfies

**r**(0)= (e^(1),0) given

**T**(t) = (-e^(cos(t)sin(t)),cos(t)), where t is an element of [0,2π]

## Homework Equations

Tangent vector

**T**=

**r**'(t)/(norm(

**r**'(t))

## The Attempt at a Solution

I was thinking that

**r**(t) = ∫

**r**'(t), and that the norm of

**r**(t) = 1; but i am having a hard time identifying a function compatible with the tangent vector that also has a norm of 1. I also attempted to find a value for t that would force the exponential aspect of -e (cos(t)sin(t)) to equal 1, while also allowing cos(t) = 0, but this did not work. Now I'm stuck second guessing myself.