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Articles : Introduction to Trigonometric Functions

With the extensive options for tracing and table-building, the Advanced Graphing app can be a useful toolbox for studying function behavior. This activity looks at the periods of trig functions.

1. Press I to open the App Library and tap on the Advanced Graphing app icon.
2. The app opens in its Symbolic view. Enter the equation Y=SIN(X) in V1, as shown in the figure to the right.
3. Press P to see the graph of the function.
4. Now tap Menu , tap Trace, select PoI (Points of Interest) and tap on Vertical Extrema, as shown in the figure to the right.
5. Now the tracer will move from extremum to extremum as you press > and <.
   The figures below show the tracer moving from left to right.
   
   Using this feature makes it easy to see that the maxima are 2π apart, the minima are also 2π apart, and the horizontal distance from one maximum to the following minimum is π.
   
   Since the Advanced Graphing app can plot relations that are not functions, the notion of tracing expands here to cover useful features such as tracing inside a region, along an edge, or between types of points of interest. As you will see next, these features are available to build tables in the Numeric view of the app.
   
   
6. Press M to switch to Numeric view. By default, the table shows a set of x- and y-values and a third column that states whether or not the (x, y) pair satisfies the expression V1.
7. Tap Trace, select PoI (Points of Interest) and tap on Vertical Extrema, just as you did in Plot view.
   Now the table shows all the extrema visible in Plot view, all at once. The minima are grouped first, followed by the maxima. To see more points, just go back to Plot view and press - to zoom out and include more extrema. The figure to the right shows the results of zooming out to include eleven extrema.
8. Press Y to return to Symbolic view and enter Y=COS(X) in V2.
9. Press P to return to Plot view. Now the PoI options under the Trace menu include Intersections with V2, as shown below. The figures show the tracer and the table in Numeric view with this option checked.

Any number of explorations are possible when you can trace and build tables with points of interest

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