coordinate system - Choosing correct proj4string in R for a set of points

I was given a set of points which I eventually will overlay with a polygon shapefile in R. The issue is that the person who provided me with the points did not give them to in long/lat coordinates but the points were already projected (I will not be able to ask them to give me the points in a better format for a while). I was given the following information about the projection of the coordinates:

Top: 583309.373443 m

Bottom: -1996690.626557 m
Left: 221989.400576 m
Right: 3572989.400576 m

Projected Coordinate System: World_Sinusoidal
Projection: Sinusoidal
False_Easting: 0.00000000
False_Northing: 0.00000000
Central_Meridian: -76.00000000
Linear Unit: Meter

Here is the head of the csv I was given:

   [,1]     [,2]
1 2413489 -1995191
2 2416489 -1995191
3 2419489 -1995191
4 2422489 -1995191
5 2425489 -1995191
6 2428489 -1995191

I need to assign the correct projection now to read these points in correctly. Here is the pro4string and SpatialPoints code I have so far:

sinu_prj <- "+proj=sinu +x_0 +y_0 +units=m +no_defs"
brazil_fish_pts <- SpatialPoints(brazil_fish_grid2,  proj4string=CRS(as.character(sinu_prj)), bbox = NULL)

I know that the proj4string code is not correct but I don't know how to fix it? Can anyone be of help?

Answer

For these kinds of things I use spatialreference.org. I searched for sinusoidal and got this for the proj4 string:

+proj=sinu +lon_0=0 +x_0=0 +y_0=0 +a=6378140 +b=6356750 +units=m +no_defs

You forgot the +lon_0 parameter which is the Central Meridian in your example (-76). This is crucial to getting the origin correct. As for the +a and +b parameters, I'm not sure how important these are in your application, but they are the semi-major and semi-minor axis of the elipsoid used. Since you don't have any information on the elipsoid used for your coordinates, you could just use these as default. So in your case I would use:

+proj=sinu +lon_0=-76 +x_0=0 +y_0=0 +a=6378140 +b=6356750 +units=m +no_defs