# Non-trigonometric parametric equation of a circle

1. Oct 2, 2012

### 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?

2. Oct 2, 2012

### 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.

3. Oct 2, 2012

### I like Serena

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

4. Oct 3, 2012

### mathman

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

5. Oct 3, 2012

### I like Serena

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