You wish to image an oblique slice located at an angle of 45o to the +Z-axis and 45o to the +Y-axis. Since gradients can only be produced with the three gradient coil systems located around the x, y, and z-axes, what combination of the three gradients should be applied to produce a slice selection, phase encoding, and frequency encoding gradient?

The slice selection gradient (Gs) should be created by a combination of y and z gradients.
Gz = Gs Sin 45o
Gy = -Gs Cos 45o

The phase encoding gradient (Gf) should be created by a combination of y and z gradients.
Gz = Gf Cos 45o
Gy = Gf Sin 45o

The frequency encoding gradient (Gf) will be equal to the x gradient.
Gx = Gf

Please note that the phase and frequency enocding gradients could be switched.