Chapter 12.3, Problem 32ES

Use the result in Exercise 31 to show the circular helix $\text{r}=a\cos t\text{i}+a\sin t\text{j}+ct\text{k}$ can be expressed as $\text{r}=\left(a\cos \frac{s}{w}\right)\text{i}+\left(a\sin \frac{s}{w}\right)\text{j}+\frac{cs}{w}\text{k}$ where $w=\sqrt{a^2+c^2}$ and s is an arc length parameter with reference point at $\left(a,0,0\right).$