We will have the following:
[tex]r=\tan ^2(\theta)\csc (\theta)\Rightarrow r=(\frac{\sin(\theta)}{\cos(\theta)})^2(\frac{1}{\sin(\theta)})[/tex][tex]\Rightarrow r=\frac{\sin^2(\theta)}{\sin(\theta)\cos^2(\theta)}\Rightarrow r=\frac{\sin(\theta)}{\cos^2(\theta)}[/tex]
Now, we corroborate with one of the expression, in our case we will analyze y = x^2:
[tex]r\sin (\theta)=(r\cos (\theta))^2\Rightarrow r\sin (\theta)=r^2\cos ^2(\theta)\Rightarrow r=\frac{\sin (\theta)}{\cos ^2(\theta)}[/tex]
So, the expression taht represents the value given is:
[tex]y=x^2[/tex]
