## Fitting a Sin Curve to Data

This applet is designed to allow a visual exploration of the problem of fitting a sin curve to given data by setting parameters.

The points "MaxPoint" and "MinPoint" can be set by dragging.  You then manipulate the parameters "a", "b", "c", and "d" with the sliders so that the curve "f(x) = a*sin(b*(x-c))+d" has "TopPoint" equal to "MaxPoint" and "BottomPoint" equal to "MinPoint".

To change the viewing area, right-click (control-click for mac people) on the open space and choose "properties" from the context menu that pops up for "Drawing Pad".  Similarly, you can type in values for the parameters by right-clicking on points on the sliders and choosing "redefine" in the pop=up menu.
 Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now) Mike May, S.J., 2/18/2006, Created with GeoGebra

Some sets of data to look at:
• Find the points that correspond to the sin(x) curve.  Set a=1, b=1, c=0, and d=0, and find values for MaxPont and MinPoint that match up.
• Find values of the parameters so that the curve has a minimum at (1,1) and a maximum at (2,2).
• Find values of the parameters so that the curve has a minimum at (2,-2) and a maximum at (4,2).
• Find values of the parameters so that the curve has a minimum at (-Pi,1) and a maximum at (Pi,2).
• Devise a rule for the values of the parameters for the curve to have:
• a minimum at (s,-1) and a maximum at (s+2*Pi,1)
• a minimum at (-Pi/2,-1) and a maximum at (-Pi/2+t,1)
• a minimum at (-Pi/2,-1) and a maximum at (Pi/2+u,1)
• a minimum at (-Pi/2,-1) and a maximum at (Pi/2,1+v)

GeoGebra is a GNUed software package for mathematics visualization.  The home for the applications is  http://www.geogebra.org.