Let (5,-6) be point on terminal side of theta

Find Sin, Csc, cot

Thanks!

Check out the image. The two triangles, one containing the origin and (5,-6) and the smaller one inside the unit circle are similar. That means the sides are in a specific ratio.

Solid blue / dotted blue = solid black / dotted black = solid red / dotted red.

All trig functions are ratios of sides within triangles.

Then the similarity factors within the trig functions will divide out.

So you have a triangle with side ratios of

A = 5, O = -6, and H = sqrt[36+25] = sqrt[61]

Then sin = O/H = -6/sqrt[61]

csc = 1/sin = -sqrt[61]/6

cot = A / O = -5/6

I hope this helps