# Convert polar coordinates to Cartesian

October 14, 2007
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(This article was first published on Quantitative Ecology, and kindly contributed to R-bloggers)

When I want to calculate the coordinates of a location (e.g., a nest or burrow) based on distance and bearing from a grid point, this function helps me avoid writing down SOH-CAH-TOA every time. Just note that the bearing in this case is from the grid point (known location) to the unknown location.

```polar2cart<-function(x,y,dist,bearing,as.deg=FALSE){  ## Translate Polar coordinates into Cartesian coordinates  ## based on starting location, distance, and bearing  ## as.deg indicates if the bearing is in degrees (T) or radians (F)    if(as.deg){    ##if bearing is in degrees, convert to radians    bearing=bearing*pi/180  }    newx<-x+dist*sin(bearing)  ##X  newy<-y+dist*cos(bearing)  ##Y  return(list("x"=newx,"y"=newy))}##Exampleoldloc=c(0,5) bearing=200 #degreesdist=5newloc<-polar2cart(oldloc[1],oldloc[2],dist,bearing,TRUE)plot(oldloc[1],oldloc[2],xlim=c(-10,10),ylim=c(-10,10))points(newloc\$x,newloc\$y,col="red")

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