c - 3d Accelerometer calculate the orientation

Question

I have accelerometer values for the 3 axes (usually when there is only gravity contains data between -1.0 and 1.0 ):

  float Rx;
  float Ry;
  float Rz;

I make some calculations, then I get the angles for each axis.

  float R =  sqrt(pow(Rx,2)+pow(Ry,2)+pow(Rz,2));
  float Arx = acos(Rx/R)*180/M_PI;
  float Ary = acos(Ry/R)*180/M_PI;
  float Arz = acos(Rz/R)*180/M_PI;

Then I set the values for the box angles in opengl

rquad = Arx;
yquad = Ary;

Which rotates my box:

glRotatef(yquad,1.0f,0.0f,0.0f);
glRotatef(rquad,0.0f,1.0f,0.0f);

It works on a hemisphere. I would like to use the full sphere and I know that I have to use the Arz value to make it work, but I don't know how can I use that for this rotation. Could you help me?

Update: The final answer is in my case:

  rquad = -atan2(Rx/R, Rz/R)*180/M_PI;
  yquad = -atan2(Ry/R, Rz/R)*180/M_PI;

Answer 1

The correct answer is:

Roll = atan2(Y, Z) * 180/M_PI;
Pitch = atan2(-X, sqrt(Y*Y + Z*Z)) * 180/M_PI;

Source: http://www.freescale.com/files/sensors/doc/app_note/AN3461.pdf (page 10, Eqn. 25 & 26)

uesp's answer is wrong. It looks like an acceptable approximation until pitch and roll both go above 45 degrees.

I may be assuming a different orientation convention, but even if you swap axes and invert values in any consistent way, uesp's computations will never be equivalent.