There are 4 possibilities here:2. x^2=(sint)^2
All are the same curve (except some can the orientation of the closed curve).
Which is a circle since,
x^2+y^2=(sin t)^2+(cos t)^2=1 [Note this is not a correct proof, because I only shown that the point lie on a circle rather than all points are on a circle].
See that x^2+y^2=14. x=(1-t^2)/(1+t^2)
So all points lie on a circle, again this does not show that all the points are the circle (which in fact is untrue). But since t>0 you see that 'y' only have positive terms so it seems to be a positive circle, that is, a semicircle.