The x dimension corresponds with the adjacent leg, and y with the opposite leg.
The hypotenuse on unit circle is 1 by definition.

sin = opp/hyp = opp on unit circle
cos = adj/hyp = adj on unit circle
tan = opp/adj
cot = 1/tan
sec = 1/cos
csc = 1/sin

So:
P(3/√(45) , 6/√(45)) = (1/√(5), 2/√(5))
sin = 2/√(5)
cos = 1/√(5)
tan = 2/√(5) * √(5)/1 = 2
cot = 1/2
sec = √(5)
csc = √(5)/2

P(-8/17, 15/17)
sin = 15/17
cos = -8/17
tan = (15/17)(17/-8) = -15/8
cot = -8/15
sec = -17/8
csc = 17/15