Yep, except you might not want the 65 degrees as your answer as that is obviously not an exact answer and is not even equivalent to your expression.
should be unitless.
If y = arctan(-5 /12),
then, tan(y) = -5/ 12
So, y is an angle whose tan value is -5 /12.
tan = (opposite side)/(adjacent side) = opp/adj
So, for angle y above,
opp = -5
adj = 12
The hypotenuse---hyp---then is sqrt[(-5)^2 +(12)^2] = 13
sec = hyp/adj
So, sec(y) = 13/12 -----you got that right.
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If y = arctan(5/(-12)),
Then, opp = 5, adj = -12, hyp = 13
sec(y) = 13/(-12) or -(13/12)