Hope this helps:
Given The unit circle, a radius can be drawn from the origin to any point on the circle in the direction of theta relative to the x axis. This creates the coordinate (x,y)
Drawing a right triangle from this gives you a horizontal length of x, vertical length of y and a hypotenuse of 1.
Use SOHCAHTOA to find tan (theta) and cot (theta):
sin(theta) = y/1 = y
cos(theta) = x/1 = x
tan(theta) = O/A = y/x = sin(theta) / cos(theta)
cot(theta) = A/O = x/y = cos(theta) / sin(theta)
