You can put this solution on YOUR website! Write as a trigonometry ratio of A, with the correct sign attached:
cosec (-A)
cosec (180+A)
cosec (180-A)
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The signs of the csc match those of the sine, since csc = 1/sin
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cosec (-A) = -csc
cosec (180+A) = -csc
cosec (180-A) = csc