Note that this is not very fast, and very memory hungry (240*2 MP images).
imgs = Table[
Rasterize[
Plot[{Sin[x Cos[a]]}, {x, -2.5 Pi, 2.5 Pi},
PlotRange -> {{-2.5 Pi, 2.5 Pi}, {-2, 2}}, Axes -> {False},
AspectRatio -> 1/4, ImageSize -> {1920, 1000},
PlotStyle -> {Directive[Thickness[.03], Black,
JoinForm["Round"]]}], "Image",
RasterSize -> {1920, 1000}], {a, Subdivide[-\[Pi], 0, 240 - 1]}];
Export["out.avi", imgs, "FrameRate" -> 60]
Alpha channel is not possible as far as I know. But any editing software will be able to easily key out the white!
A better way (generally) is to export separate image files, and load these into your favorite video editing software, it will be much faster, smaller video-files, and saving separate image files is way less memory hungry... (the output file was 1.38 GB on my machine!!).