Are your transforms 'full 3d' or 'half 3d'? That is, when your character rotates, can they rotate over all axes, or just around an 'up' vector? Are you using matrices as the authoritative representation of the character's transform, or some scalars ( typically x, y,z and rotation ).
MATRICES
If you're using transform matrices, the vector that points 'forward' in the character's space is one of the vectors in the upper 3x3 submatrix, the actual vector depends on the way you define 'up' and 'forward', and whether the vector is a row or column of the matrix depends on whether you treat vectors as rows or columns.. but for e.g., in OpenGL, it would usually be:
m00 m01 m02 m03
m10 m11 m12 m13
m20 m21 m22 m23
m30 m31 m32 m33
the usual 'forward' vector (z) is emboldened. If you extract 'forward' from the character's matrix, and add if to the character's position, it will move the character in their own 'forward'.
I know for a
fact that this is different in most DX setups, but it will be quite similar, most likely the row m20->m22, assuming that z is forward, which it isn't always.
SCALARS
If you're just using x, y, z and rotation scalars.... then assuming that positive z is 'up' and positive x is 'forward'... the forward direction vector is:
x = cos ( r )
y = sin ( r )
so,
player.x += cos ( r ) * speed;
player.y += sin ( r ) * speed;
should work. if it comes out sideways ( i.e moving to the left/right rather than back/forward, then change to cos ( r + ( pi / 2 ) ) and sin ( r + ( pi / 2 ) ), or minus, perhaps multiply all by -1: it all depends on how you interpret components in your code.
Unsolved 
a quick hint would be appriecated. 
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