Q: My Tangent to Cylinder workplane is at some arbitrary angle (3507)

A: Most likely you are using a edge/axis modifier option to make your workplane as well as a tangent option. What s really happening here is that you are creating a workplane tangent to your cylinder that passes through the 0,0,0 of your world coordinate system. You should be using a planar parallel option instead of Edge/Axis. See the other FAQ in this category on how to make a tangent workplane