Equation of Unit Circle

Theorem

Let the unit circle have its center at the origin of the Cartesian plane.

Its equation is given by:

$x^2 + y^2 = 1$

This article is complete as far as it goes, but it could do with expansion. In particular: Present it in polar coordinates as well You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Proof

From Equation of Circle, the equation of a circle with radius $R$ and center $\tuple {a, b}$ is:

$\paren {x - a}^2 + \paren {y - b}^2 = R^2$

Substituting $\tuple {0, 0}$ for $\tuple {a, b}$ and $1$ for $R$ gives the result.

$\blacksquare$

Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 3$. Roots of Unity
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): polar equation