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 opposite direction from ,
starting from and moving back 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 x-axis.
If two points, such as and , are symmetric about the x-axis,
- How must their x-coordinates be related?
- How must their y-coordinates be related?
The graph above illustrates the x-axis symmetry displayed by the angles
and
Pairs of points that are symmetric about the x-axis will always:
- have the same x-coordinates
- have y-coordinates that are the negative of one another
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/