Sketch the vector equation:$ r(t) = (2\cos(t), 2\sin(t), 1)$

Question

Given the parametric equations: $$x = 2\cos(t), \quad y=2\sin(t), \quad z = 1.$$

We know that $x^2 + y^2 = 4\cos^2(t) + 4\sin^2(t) = 4(\cos^2(t) + \sin^2(t)) = 4$.

In other problems, I've seen this fact tell us that the graph lies on the cylinder $x^2 + y^2 = 4$. However, in this case, $z$ is a constant. Does this mean that the 3D graph looks like a circle with radius of $2$, at $z = 1$?

Answer 1

Yes, you are correct, circle at z = 1

Answer 2

You are right and this is the circle.