Unit Circle: Origin Symmetry
Symmetry in Trigonometry
The green slider determines the angle , with a range of to .
After using the green slider to vary the angle a bit, what function of do you think
describes the angle in the graph below? moves in the same direction as ,
starting from and moving towards .
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 x-coordinates be related?
- How must their y-coordinates be related?
The graph above illustrates the symmetry about the origin displayed by the angles
and
Pairs of points that are symmetric about the origin will 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/