Tangent Vector for r=sint, theta=t/3

[dylanhouse]

Homework Statement

Find the tangent vector and unit tangent vector for the curve: r=sint, theta=t/3 for 0<=t<=6pi.

Homework Equations

If the tangent vector is r'(t)e(hat)r + r*theta(t)e(hat)theta, how does the restriction on t affect the answer? The same for the unit tangent vector, they don't seem to rely on this restriction.

The Attempt at a Solution

 

[Orodruin]

You are correct, the tangent vector at a given t does not depend on the range of t, only on the value of t chosen. The only relevance I see of the chosen range is that it closes the curve.