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If θ is in Quadrant IV and sinθ = - 5/13, then secθ =

A. - 13/12

B. - 12/13

C. 12/13

D. 13/12

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)

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