[b]Symmetry in Trigonometry[/b][br][br][b]The green slider[/b] determines the angle [math]\alpha[/math], with a range of [math]-90^o [/math] to [math]90^o [/math].[br][br]After using the green slider to vary the angle [math]\alpha[/math] a bit, what function of [math]\alpha[/math] do you think[br]describes the angle [math]\beta[/math] in the graph below? [math]\beta[/math] moves in the opposite direction from [math]\alpha[/math],[br]starting from [math]180^o[/math] and moving back towards [math]0^o[/math].

The angle [math]\beta[/math] is equal to [math](180^o -\alpha)[/math].[br][br]Move the green slider to the left and right, and watch how points [math]P_1[/math] and [math]P_2[/math] are always [br]symmetrical to one another about the [i]y[/i]-axis. [br][br]If two points, such as [math]P_1[/math] and [math]P_2[/math], are symmetric about the [i]y[/i]-axis,[br]- How must their [i]x[/i]-coordinates be related?[br]- How must their [i]y[/i]-coordinates be related?[br][br]The graph above illustrates the [i]y[/i]-axis symmetry displayed by the angles[br][math]\;\;\;\;\;\;\alpha\;\;[/math] and [math]\;\;180^o -\alpha[/math][br][br]Pairs of points that are symmetric about the [i]y[/i]-axis will [b]always[/b]:[br]- have [i]x[/i]-coordinates that are the negative of one another[br]- have the same [i]y[/i]-coordinates[br][br]Note that negative angles are displayed as their positive equivalents.[br][br]If you wish to use other applets similar to this, you may find an index of all my applets here: [url=https://mathmaine.wordpress.com/2010/04/27/geogebra/]https://mathmaine.com/2010/04/27/geogebra/[/url]