Graph Vector Function r(t) = sin t (i) + cos t (j) + t (k)

[afcwestwarrior]

Homework Statement

r(t) = sin t (i) + cos t (j) + t (k)

(a) Graph the vector function

i = x

j = y

k = z


Is this correct.

Since t is in the Z direction. I'm going to assume that this graph is parallel to the XY plane.


Now I'll take

x = sin t
y = cost t

Then if you square both of these functions.

so then we get x^2 + y^2 = (sin t) ^ 2 + (cos t) ^ 2

Then this becomes x^2 + y ^2 = 1

So it's a circle. Right. Is it going to be a spring or coil on the z - axis.

 

[jdougherty]

Yep, that's right. The term for such a graph is a "helix".

 

[afcwestwarrior]

Oh ok. Thanks.