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!!).