The point (5/13,y) in the fourth quadrant corresponds to angle θ on the unit circle.
sec θ =
cot θ =

Cos θ = adjacent / hypothenus = 5/13
opposite = sqrt(hypothenus^2 - adjacent^2) = sqrt(13^2 - 5^2) = sqrt(169 - 25) = sqrt(144) = 12

sec θ = 1/cos θ = 1/(adjacent / hypothenus) = hypothenus / adjacent = 13/5
cot θ = 1/tan θ = 1/(opposite/adjacent) = adjacent / opposite = 5/12

sec θ = 13/5
cot θ = 5/12

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