## 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.

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.

Return to the GeoGebra Applet page.

Return to the
Applets for courses below calculus page.

Return to the Calculus
Applet page.

Last updated By Mike May, S.J.,
August, 2007.

Converted to GeoGebra 5 by Mike May, S.J.,
May, 2016.