Tangent Vectors

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Page ID: 91751

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Observing the Tangent Vectors of a Vectors Valued Function

Below shows the graph of a vector valued function, but a vector values function is more than just a static graph. If you hit the Animate button, you will see the tangent vector move and change as time, \(t\) progresses. You can also choose to observe the unit tangent vector.

\(\vecs{r}(t)=<t, \frac{1}{3}t^2>, -3<t<3\)

\(\vecs{r}(t)=<\frac{5\cos(t)}{t}, \frac{5\sin(t)}{t}>, 1<t<30\)

\(\vecs{r}(t)=<3\cos(5t)\cos(t), 3\cos(5t)\sin(t)>, 0<t<4\)

\(\vecs{r}(t)=<2\sin(t), 4\sin^2(t)>, 0<t<10\)

\(\vecs{r}(t)=<t^2, e^{t/2}>, -3<t<3\)

\(\vecs{r}(t)=<3\cos(-t), 4\sin(-t)>, 0<t<10\)

\(\vecs{r}(t)=<t\cos(t), t\sin(t)>, 0<t<7\)

\(\vecs{r}(t)=<t^2, \frac{1}{3}t^3>, -2<t<2\)

\(\vecs{r}(t)=<e^t, e^{-t}>, -2<t<2\)

\(\vecs{r}(t)=<\frac{10}{1+t^2}, \frac{10}{1+t^4}>, -1<t<3\)

Tangent Vector Unit Tangent Vector