Your terminology is awful

cot - 8/17 is meaningless

I will assume you were given cot Ø = -8/17 and are asked to find the remaining 5 trig ratios

if cot Ø = -8/17, then tan Ø = -17/8

you should also have memorized the 3 main trig functions in terms of x, y, and r

e.g. tan Ø = y/x = -17/8 ---> terminal point (8, -17)

or

tan Ø = y/x = 17/-8 ----> terminal point (-8,17)

From the CAST rule we know that Ø must be either in quadrants II or IV , as seen from the position of the terminal arm points.

so make appropriate sketches showing right-angled triangles .

x^2 + y^2 = r^2 , taking one of the points

r^2 = 8^2 + (-17)^2

r^2 = 353

r = √353 , (r is always positive)

sinØ = y/r = 17/√353 or sinØ = 17/√353

cosØ = ±8/√353 so

secØ = ± √353/8

etc using the basic definitions.

Let me know if my assumption was not correct