How can I input a continuous value range in blender?

Question

General Explanation to My Question

I want to display a curve defined by parameter equations using a shader node tree:

$$ f(x)=\left\{ \begin{aligned} x & = f(\theta) \\ y & = g(\theta) \\ \end{aligned} \right. $$

To achieve this, I have to input a precise range of $\theta$ in the Shader Editor.

The situation

I've created something interesting: a screen that displays a Lissajous curve. Here is how my node tree look like:

The node tree mainly comprises of 2 parts:

1. the coordinate grids
2. the curve (or, to be more precise, "the dot")

Here is what my texture looks like on a plane (2m * 2m, layed on XOY Plane) :

The question

Currently, I use a Value node which outputs #frame to change the position of the dot along with time of animation, just like a oscilloscope in the real world.

But I'd like to go furthur - I want to show the curve all at once, that is, to show the entire curve in one frame.

A common definition of Lissajous Curve is given as: $$ f(x)=\left\{ \begin{aligned} x & = \sin(\theta) \\ y & = \sin(\omega \theta + \phi) \\ \end{aligned} \right. $$

To display this, I have to input a range of $\theta$ in the Shader Editor. And to the best of my knowledge, this is impossible unless an output node, like the Value, is capable of outputing a "continuous" value range.

Is there any way I can output a value range, or is there any workaround? Thanks a lot!