Parametric Representation of a Helix

[SlideMan]

Just wanted to check and see if this is right. The k-component of the vector is what I'm unsure of...I've always sucked at converting to parametric form. :)

Homework Statement

Convert to parametric form:
$$x^{2}$$ + $$y^{2}$$ = 9, z = 4arctan(y/x)

The Attempt at a Solution

The i- and j-components of the vector are obviously 3cos(t) and 3sin(t), respectively. I'm not sure how the k-component is supposed to turn out...

Here's my attempt:

x = 3cos(t)
y = 3sin(t)
So, z = 4 arctan $$\frac{3sin(t)}{3cos(t)}$$ = 4 arctan(tan(t)) = 4t

Thus, r(t) = [3cos(t), 3sin(t), 4t]

 

[vector3]

Looks good to me.