If the angle theta is in Q IV, then the adj. side is + and the opp side is - . The hyp is always + .
If sin theta = -5,13, then we know that the opp side is -5, and the hyp is +13.
The adj. side is found as follows: sqrt(13^2 - (-5)^2 ), which here is sqrt(169 - 25), or plus or minus 12. As before, in Q IV the adj side is +, so choose +12.
Then sec theta = hyp / adj = 13/12 (answer)
