Unit Circle: x-axis Symmetry
- Whit Ford
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/