Re: Formula for Frequency shift at stationary observer off plane of motion.

to answer your question, let us start with a simple thought experiment. 
imagine a source emitting a constant pitch sound rotating in a circle. will 
a detector at the centre of the circle detect a change in pitch?

the answer is no, and that is because the straight line distance between 
emitter and detector is not changing with time. this is because the 
velocity of the source is always perpendicular to the line joining it and 
the detector, and therefore there is no component of it's velocity along 
this line.

so, to calculate the frequency shift, all you have to do is to resolve the 
velocity of the source along the instantaneous straight line direction 
between source and observer, and then plug this component into the regular 
formula.

in your example, this component changes with time because the angle that 
the straight line between source and observer makes with the line of motion 
of the source changes with time. so the frequency shift itself will be 
different at different times. it must be obvious to you now that the 
observer will detect the true pitch when the source is exactly in front of 
the observer.

now, a question for you. will the last result hold for a light source 
moving at relativistic speeds?