Question

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Answer 1

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)

Answer 2

 the length of the  adjacent side will be 12 
so cos theta  will equal  12/13 

sec theta = 1 / cos theta will be 13/12 Answer

Its D