Three trigonometric functions for a given angle are shown below csc theta = 13/12, sec theta = -13/5, cot theta = -5/12 what are the coordinates of point (x, y) on the terminal ray of angle theta, assuming that the values above we’re not simplified.

We have that
csc ∅=13/12
sec ∅=-13/5
cot ∅=-5/12

we know that
csc ∅=1/sin ∅
sin ∅=1/ csc ∅------> sin ∅=12/13

sec ∅=-13/5
sec ∅=1/cos ∅
cos ∅=1/sec ∅------> cos ∅=-5/13

sin ∅ is positive and cos ∅ is negative
so
∅ belong to the II quadrant

therefore
the coordinates of point (x,y) on the terminal ray of angle theta are
x=-5
y=12

the answer is
point (-5,12)

see the attached figure

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°