Draw a right triangle and mark an angle q



We look at the first equation

x = 

Since the cosecant is the hypotenuse over the opposite, and
since x can be written as  and x = ,
we can put x as the length of the hypotenuse and 1 as the 
length of the opposite.



And by the Pythagorean theorem we can get the adjacent side

     c² = a² + b²
     x² = a² + 1²
     x² = a² + 1
 x² - 1 = a²

√x² - 1 = √a²

√x² - 1 = a

We label the length of the adjacent side



Now we look at the second equation

y = 

The cotangent is the adjacent over the opposite, so we substitute
 for cot(q) or just .

in the second equation:

y = 

Edwin