Ttyjfyk

How do I get the InputField to coordinate with the LocatorPane so that a change in each control changes the other to be in agreement? It would be nice if the function was self-contained and was dynamically linked to a second similar control where the variable is radians. The angle control is based on this (see Applications). Related links do not address or solve this particular issue; links such as this this, and this

 fDeg[Dynamic[angleDeg_]] := 
 DynamicModule[p, angleRad, angleCalc, dtr = Degree, 

 angleCalc[newp_, 
 oldp_] := (angleRad = 
 angleRad + ArcCos[newp.oldp] Sign[Cross[newp].(newp - oldp)]; 
 If[0 < angleRad, angleRad = Mod[angleRad, +2*Pi]]; 
 If[0 > angleRad, angleRad = Mod[angleRad, -2*Pi]]; 
 angleDeg = angleRad/dtr; 
 f[angleDeg]; 
 p = Cos[angleRad], Sin[angleRad]); 

 angleRad = angleDeg*dtr; 
 p = Cos[angleRad], Sin[angleRad]; 

 LocatorPane[Dynamic[p, (angleCalc @@ Normalize /@ #, p) &], 
 Dynamic@Show[ 
 Graphics[Circle[], Arrowheads[0.15], 
 Arrow[Dynamic[0, 0, p]], ImageSize -> Tiny], 
 Graphics[Dynamic[Text[ 
 NumberForm[angleDeg, 3, 2], 0, 0]]]], 
 Appearance -> None]]; 

 aDeg = 45; 

 Column[ 
 "Degrees:", 
 fDeg[Dynamic[aDeg]], 
 "aDeg: ", 
 InputField[Dynamic[aDeg], 
 FieldSize -> 6] 
 , Alignment -> Center] 

Consider the following refactoring of your code

First, the locator pane is used to set a point location constrained on a circle with unit radius (this part borrowed heavily from an example in the documentation for LocatorPane). A degree value is then calculated from the coordinates of tha tpoint.

Secondly, the input field is used to read in a degree value, which is then used to update the position of the dynamic point pt using the second argument of Dynamic.

DynamicModule[
 pt = 0, 1.,
 Column[
 "Degrees:", Dynamic[(ArcTan @@ pt)/Degree],
 LocatorPane[
 Dynamic[pt],
 Graphics[
 Circle[],
 PointSize[Large],
 Dynamic[Arrow[0, 0, pt/Norm[pt]]]
 ],
 Appearance -> None
 ],
 InputField[
 Dynamic[(ArcTan @@ pt)/Degree, (pt = N@Cos[#1 Degree], Sin[#1 Degree]) &],
 FieldSize -> Tiny
 ]
 , Alignment -> Center
 ]
]

This keeps both fields in sync with each other: