Cheap wide angle lenses?

What could be a cheap but effective wide angle lens? I like to focus on landscapes and at times star trails.
Shooting on a Nikon D3200.

Depends. What's your definition of cheap? I'd say if you're looking for something under $500 (cheap for a good wide angle lens), then go to keh.com and check out what they've got used. When buying cheap, you'll a better lens used than the comparably priced new lens.

You're going to want to get a good prime or ultra-wide zoom. Regardless which you choose, you will also need a fast lens. This isn't an issue with primes as they're almost always fast with an aperture of f/2.8 or better. Zooms, on the other hand, often aren't that fast unless you spend a good bit of coinage.

I'd say check out keh for a good prime wide angle lens that has a large f/2.8 or larger (e.g. F/2) lens.

To see just how much sharper one lens is over another, go to photozone.de

You can look at Tokina 12-24 mm or 11-16 mm wide angle zoom lenses.

They are well built and have fine optics.

The 12-24 mm f/4 Tokina costs about $320 used and a new 11-16 mm f/2.8 about $400

The term "cheap" refers to poorly designed and made products. Tokina lenses are inexpensive, but NOT cheap

Samayan 8mm f/3.5 is ultrawide, as it's fisheye. Cost less than $300, lesser for the 2nd hand one.

BTW, it's manual focus. However, by its fisheye nature, you almost need no focus. Every thing, from 3 feet away to infinity, is in focus.

Almost every good photo editing software can do "de-fish" the picture and give you straight, wide picture.

No need to de-fish in case of star shooting.

The 18-55m kit lens is wide angle from 18-24mm. Since you already have it, it's free.