Just checking.lens and focal lengths?

I have a sigma DG 70-200mm 2.8 HSM II lens on a nikon d90… I should be getting a 1.5 crop factor, correct? Making the effective focal range 105-300mm? I was fairly sure this was a full frame lens but am getting no crop factor, as 200mm on this lens is the same as on my nikkor 55-200mm 4.5-5.6 VR.

Oh, and you were doing so close, right until the end. The 200mm on the nikkor gets the same crop factor as the 200mm on the sigma. Crop factor is a body "function" so it affect all lenses equally.

The crop factor is the the size of the sensor (vs a 35mm sized sensor) so its part of the camera. It affects any lens you bolt to the front.

Both of your lenses will 'crop' to the same degree.

So called full frame (or FX) lenses can be used on full frame cameras without any loss of image quality caused by the camera only using the central portion of the sensor (which is what happens with Nikon when you mount a DX lens on an FX body).

From your question, it is very apparent that you have never taken a class in photography. These questions are answered in the first couple of lectures, but better, a formal class in photography helps you develop skills you can use with any camera you may later hold and gives you all the tools to figure these kinds of things out.

At 200 mm, both cameras will give you the same angle of view.

I'm sure that you are noticing that using the "try and fail" method is not serving well at all.

Your Nikkor 55-200mm lens on your D90 will have the same angle of view as an 82.5-300mm lens on a 35mm film camera or full-frame DSLR.

Your Sigma 70-200mm lens on your D90 will have the same angle of view as a 105-300mm lens on a 35mm film camera or full-frame DSLR.