Trig Equation of a Circle I was trying out derivatives of inverse functions(I'm new to that) which led me to this. I graphed the equation $y=\sin\left(\cos^{-1}(x)\right)$. This is a half circle and squaring both sides gives a full unit circle. Except for $y=\sin\left(\cos^{-1}(x)\right)$ and $x^2+y^2=1$, are there any other interesting forms of the equation for a circle with radius 1 and the center at the origin.
Also, do these two forms relate to each other in any way?

The simplest and simultaniously the deepest equation for the unit circle is $$r=1$$ in polar coordinates.
