A ratio that is equivalent is 18:48
The reciprocal cosine function is secant: sec(theta)=1/cos(theta). The reciprocal sine function is cosecant, csc(theta)=1/sin(theta). The reciprocal tan function is cotan
Cotx=1\tanx

Then using trygonometric table or a graph we read that:

Period of cosinus function = 2π
So the last answer is
Answer:
From the question we are told that
The equation is 
Generally the goal of this solution is to prove that the implicit solution of the differential equation above is 
First Step
Differentiate the solution with respect to x
![0 = \frac{2x}{ x^2 + 11} + [-cot * csc(y) ]\frac{dy}{dx}](https://tex.z-dn.net/?f=0%20%20%3D%20%5Cfrac%7B2x%7D%7B%20x%5E2%20%2B%2011%7D%20%20%2B%20%5B-cot%20%2A%20csc%28y%29%20%5D%5Cfrac%7Bdy%7D%7Bdx%7D)
=>
=> ![0 = \frac{2x}{ x^2 + 11} + [-\frac{cos(y)}{ sin^2(y) }]\frac{dy}{dx}](https://tex.z-dn.net/?f=0%20%20%3D%20%20%5Cfrac%7B2x%7D%7B%20x%5E2%20%2B%2011%7D%20%20%2B%20%5B-%5Cfrac%7Bcos%28y%29%7D%7B%20sin%5E2%28y%29%20%7D%5D%5Cfrac%7Bdy%7D%7Bdx%7D)
=>
multiply through by
,
, 
So
=>
Looking at the equation obtained we see that it is equivalent to the differential equation hence the implicit solution of
is 
Step-by-step explanation: