Clear, simple way to determine Side of Phi in Angle Calculation I have to think of a better title. This really is a simple situation. 
So, I have a joystick, and a player character.  I am calculating the angle of direction by comparing the joystick position to the orientation of the character. 
The character has an angular rotation about the vertical axis (in 3d).  Using that angular rotation, I have a unit vector $$heading = (cos(\theta),sin(\theta))$$ that represents the character's heading. 
Next, I have a joystick vector $$(X,Y)$$ where X and Y are the displacements from 1 to -1  of the horizontal and vertical axis of the joystick.  I normalize this vector, so: $$xnorm = (X',Y')$$
And then I take the dot product, divide by magnitude of $xnorm$ in case of flow over 1.0, and take the inverse cosine of the result. 
And here is my problem: the inverse cosine returns the values fine...however, I have no minus sign for which side of the heading the joystick is on...everything is just the absolute value of $\phi$. 
So, is there an easy way to determine which side of the heading the joystick vector sits on, so I can label with a minus sign?

Compute $\sin\phi=X'\sin\theta-Y'\cos\theta$: if $\sin\phi>0$ then $xnorm$ must rotate counterclockwise to reach $heading$, if $\sin\phi<0$ it must rotate clockwise.
