### Instruction: For a constant $c,$ in cylindrical coordinates $(r,\theta,z),$ find the shape described by the equation
\[\theta = c.\](A) Line
(B) Circle
(C) Plane
(D) Sphere
(E) Cylinder
(F) Cone

Enter the letter of the correct option.### Response: I recall that in cylindrical coordinates, $\theta$ is the angle in the $xy$-plane measured from the positive $x$-axis, so $\theta$ is constant on any ray from the origin in that plane.
Therefore, the equation $\theta = c$ means that all the points have the same angle $c$ in the $xy$-plane, regardless of their $r$ and $z$ values.
That means the shape is a plane that contains the $z$-axis and makes an angle of $c$ with the $x$-axis.