Visualizing a Parametric Equation in 3D Space

[CourtneyS]

Homework Statement

Given the eqn x=2, y=sin(t), z=cos(t), draw this function in 3-space.

Homework Equations

ABOVE^

The Attempt at a Solution

I did this:
x^2+y^2+z^2=2^2+(sin(t))^2+(cos(t))^2=5
Therefore we get x^2+y^2+z^2=5
Which is the eqn of a sphere with radius root5.

My friend said it's supposed to be a circle but I can't see how?
Which one of us is right if either.

 

[phyzguy]

If x is always equal to 2, how can it be a sphere?

 

[CourtneyS]

If x is always equal to 2, how can it be a sphere?

:(

 

[haruspex]

:(

Another way of looking at it... there is only one degree of freedom (t), so it must be a line, not a surface.