Non-trigonometric parametric equation of a circle

[johann1301]

I wish to write this equation:

1=√(x²+y²)

as a parametric equation but WITHOUT the use of sine and cosine.

Is this possible?

 

[Vorde]

I don't think so. You could use the maclauren series for sine and cosine, but you'd need an infinite sum for it to be completely correct.

Edit: A generic circle can be drawn in the complex plane without sine/cosine, but it wouldn't be whatsoever equivalent to the formula you gave.

 

[I like Serena]

There is another parametrization:
$$x={1-t^2 \over 1+t^2}$$
$$y={2t \over 1+t^2}$$

 

[mathman]

There is another parametrization:
$$x={1-t^2 \over 1+t^2}$$
$$y={2t \over 1+t^2}$$

Almost - this is a semicircle. -1<t<1.

 

[I like Serena]

Almost - this is a semicircle. -1<t<1.

It's a little more with $t \in \mathbb R$, or even better with $t \in \mathbb R \cup \{\infty\}$.