If sin theta < 0 and tan theta > 0 as described in the task content, then, cos theta < 0 and 180<theta <270.
From the task content, it was described that sin theta < 0 and tan theta > 0.
Upon recall of angle quadrants, it follows that only the 3rd quadrant angles have positive tan values and negative sin values. Hence, it follows that the angle theta is in the 3rd quadrant and also has cos theta < 0.
Read more on quadrants;
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