# Unit Circle: Origin Symmetry

- Author:
- Whit Ford

- Topic:
- Circle, Symmetry, Trigonometry, Unit Circle

**Symmetry in Trigonometry**The green slider determines the angle

The angle is equal to .
Move the green slider to the left and right, and watch how points and are always
symmetrical to one another about the origin.
If two points, such as and , are symmetric about the origin,
- How must their and
Pairs of points that are symmetric about the origin will

*x*-coordinates be related? - How must their*y*-coordinates be related? The graph above illustrates the symmetry about the origin displayed by the angles**always**:: - have*x*-coordinates that are the negative of one another - have*y*-coordinates that are the negative of one another Note that negative angles are displayed as their positive equivalents. If you wish to use other applets similar to this, you may find an index of all my applets here: https://mathmaine.com/2010/04/27/geogebra/