If coT c = - radical 15 and <C is in quadrant IV, find csc C.
Draw the x,y-plane.
Draw a right triangle in the fourth quadrant, with the triangle "hanging" from the x-axis (that is, with one leg being on the positive x-axis). Label the angle at the origin as "C".
Use what you know about the cotangent ratio to label the two legs of the triangle, noting that the y-value must be negative, and using the fact that:
. . . . .
Then use the Pythagorean Theorem to find the length of the hypotenuse.
Now that you have all three sides labelled, read off the value of the cosecant.