(1) find the torsion of the helix a(t) = (cos(t), sin(t), t)

The torsion of the helix is .

Step-by-step explanation:

To complete this exercise we need to recall the formula for the torsion of a curve. Given a parametrization the torsion of the curve is given by

.

So, the first step is to find the derivatives of the vector function .

Thus,

,

,

,

.

Now, we must calculate the cross product of the vector functions and .

.

Now we calculate :

Recall that the norm of a vector in the space is

.

At this point we have

.

d

gimmee one of those gold crowns!

~coco