Plotting 3d geometry using sin cos

I’m interested in using Unity for more than just games. Things like data visualization, installation work, interfacing with sensors, etc. I came across a book full of formulas for 3d geometric patterns using sin and cos.

Can anyone tell me how I might translate these formulas into actual visible 3d patterns in Unity?

Your best bet would be to take advantage of the GL object. This allows you to use lower-ish level OpenGL commands to build procedural meshes. See the unity documentation for more information/examples on this object: Unity - Scripting API: GL