Actually R2000, they're not related. If you know the crosswind component only, you cannot figure out the headwind component. For example, if the wind is 60 degrees off the nose at 10 knots, then the crosswind component is 10*sin(60) = 8.67 knots. However, if all you know is the crosswind component, for example 8.67 knots, then this could equate to zero headwind if the actual wind is a 90 degree crosswind at 8.67 knots, or it could equate to a headwind of 5.00 knots (10*cos(60) = 5 knots) if the actual wind is 60 degrees off the nose at 10 knots. In fact, if all you know is the crosswind component, there is an infinite number of wind/angle possibilities that fit this crosswind component.
Hawk