It will be easier if you use vector notation in figuring out the formulae. Call your two end points P, Q, you only need to find one displacement vector, say from P to top right corner, call that vector v, then the four corners are given by:
P + v, P - v, Q + v, Q - v
Note that the tangent of an angle is just the slope of the line(i.e., (y2-y1)/(x2-x1)), and when two lines are perpendicular, their slopes are negative reciprocal of each other. Using these facts, you won't really need to use sine/cosine, just tangent.
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