# Why is a circle 1-dimensional?

In the textbook I am reading, it says a dimension is the number of independent parameters needed to specify a point. In order to make a circle, you need two points to specify the $x$ and $y$ position of a circle, but apparently a circle can be described with only the $x$-coordinate? How is this possible without the $y$-coordinate also?

$$(\sin(\theta),\cos(\theta))$$
which uses only one parameter. We could also notice that there are only $2$ points with a given $x$ coordinate:
$$(x,\pm\sqrt{1-x^2})$$