Question

Use a computer to graph the curve described by the function. $$ \begin{array}{l} \mathbf{r}(t)=\frac{1}{2} \sin t \mathbf{i}+\frac{1}{2} \cos t \mathbf{j}+\frac{t^{2}}{100 \pi^{2}} \mathbf{k}, \quad 0 \leq t \leq 10 \pi\\ \text { (Fresnel integral spiral) } \end{array} $$

          Use a computer to graph the curve described by the function. 
$$
\begin{array}{l}
\mathbf{r}(t)=\frac{1}{2} \sin t \mathbf{i}+\frac{1}{2} \cos t \mathbf{j}+\frac{t^{2}}{100 \pi^{2}} \mathbf{k}, \quad 0 \leq t \leq 10 \pi\\
\text { (Fresnel integral spiral) }
\end{array}
$$

Added by Jennifer C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suman Saurav Thakur

Step 1

First, we need to plot the x and y coordinates of the curve. We can use the parametric equations for x and y: $$ x(t) = \frac{1}{2} \sin t, \quad y(t) = \frac{1}{2} \cos t $$ Show more…

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Use a computer to graph the curve described by the function. $$ \begin{array}{l} \mathbf{r}(t)=\frac{1}{2} \sin t \mathbf{i}+\frac{1}{2} \cos t \mathbf{j}+\frac{t^{2}}{100 \pi^{2}} \mathbf{k}, \quad 0 \leq t \leq 10 \pi\\ \text { (Fresnel integral spiral) } \end{array} $$