# Compute the unit tangent vector T(t) to the position vector r(t) = \langle \cos 3t, \sin...

## Question:

Compute the unit tangent vector {eq}\mathbf T(t) {/eq} to the position vector {eq}\mathbf r(t) = \langle \cos 3t, \sin 3t \rangle {/eq} at {eq}t = \frac{\pi}{4} {/eq}

## Unit tangent vector:

Unit tangent vector {eq}T (t) {/eq} is the derivative of the position vector divided by the length of the position vector at a given point.

The unit tangent vector {eq}T (t) = \frac{r (t)}{ |r (t)\prime| } {/eq}

The derivative of the position vector r(t) is {eq}r (t)\prime = \langle...

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