Question

A helix is a three dimensional spiral. The coiled strands of DNA and the edges of twisted crepe paper are examples of helixes. In the diagram, the y-coordinate of each edge illustrates a cosine function. Write an equation for the y-coordinate of one edge.

Answer 1

You want to find a function of the form \(y=a\cos(bx)\).

\(|a|\) would be the amplitude, and \(b\) determines the period of the function. The period of such a function is given by \(\dfrac{2\pi}{b}\).

From the picture, you can gather that \(a=1\) and that the period is 24.

So, you have
\[\frac{2\pi}{b}=24~~\iff~~b=\frac{\pi}{12}\]
The function would be \(y=\cos\dfrac{\pi x}{12}\).