Trig question: How to find theta, given X and Y when X and Y are both negative

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Trig question: How to find theta, given X and Y when X and Y are both negative

Mathematics
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|dw:1437664037564:dw| For reference
mental gymnasitics ... the trig functions give us an angle in relation to the x axis so we have to make adjustments
if given an x and y, it tends to be tan related ..

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CLARIFICATION: if Y is positive, we can use arccos(x/radius) to find theta, if X is positive, we can use arcsin(y/radius) to find theta Is there an easy way like this to find theta if both are negative? (preferably in very few steps, to make it easy for a computer program to calculate quickly)
arctan( ) has range -pi/2 to pi/2 which means to find theta in the 1st and 4th quadrant we can just do arctan( y/x)+2pi*n I put the +2pi*n depending on the domain of theta n is an integer now the tricky part is what to do when we get to the 2nd and 3rd quadrant if we try doing arctan(y/x) for these two quadrants y/x will be positive if we are in the third quadrant which means arctan(y/x) will really being giving us outputs from the 1st quadrant so we can add pi or even pi+2pi*n or factoring out the pi ... pi(1+2n) something similar happens for the 2nd quadrant |dw:1437667271475:dw| choosing the integer n depends on the domain of theta

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