Create an applet with the sine function and graph its derivative through the slope of the tangent in each point.

[list=1][*]Move point [i]A[/i] along the function graph and make a conjecture about the shape of the path of point [i]S,[/i] which corresponds to the slope function.          [br][/*][*]Turn on the [img]https://wiki.geogebra.org/uploads/thumb/e/e2/Menu-trace-on.svg/16px-Menu-trace-on.svg.png[/img] trace of point [i]S[/i]. Move point [i]A[/i] to check your conjecture.[br][b]Hint:[/b] Right-click point [i]S[/i] (MacOS: [i]Ctrl[/i]-click, tablet: long tap) and select [img]https://wiki.geogebra.org/uploads/thumb/e/e2/Menu-trace-on.svg/16px-Menu-trace-on.svg.png[/img] [i]Show Trace[/i].[/*][*]Find the equation of the resulting slope function and enter it into the [i]Input Bar [/i]using [i]g(x) = ... .[/i] Move point [i]A[/i] along the graph of function [i]f[/i]. If your prediction is correct, the trace of point [i]S [/i]will match the graph of your function [i]g[/i].[br][/*][/list]

[table][tr][td][size=100]1.[/size][/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][br][/td][td][size=100]Enter the function [code][/code][code]f(x) = sin(x)[/code].[/size][/td][/tr][tr][td][size=100][/size][br][/td][td][icon]https://wiki.geogebra.org/uploads/thumb/3/30/Menu-options.svg/120px-Menu-options.svg.png[/icon][br][/td][td][size=100]Right-Click on the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i] and select [i]Graphics...[/i] . Select tab [i]xAxis[/i] and change the unit to [math]\pi.[/math][/size][br][/td][/tr][tr][td][size=100]2.[/size][/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_pointonobject.png[/icon][br][/td][td][size=100]Create a new point [i]A[/i] on function [i]f[/i].[br][b]Hint: [/b]Point A can only be moved along the function.[/size][/td][/tr][tr][td][size=100]3.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_tangent.png[/icon][/size][/td][td][size=100]Create tangent [i]g[/i] to function [i]f[/i] through point [i]A[/i].[/size][/td][/tr][tr][td][size=100]4.[/size][/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_slope.png[/icon][br][/td][td][size=100]Create the slope of tangent g using the [i]Slope[/i] tool.[/size][/td][/tr][tr][td][size=100]5.[/size][/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][br][/td][td][size=100]Define point [code]S = (x(A), m)[/code].[br][b]Hint:[/b] [code]x(A)[/code] gives you the [i]x[/i]-coordinate of point [i]A[/i].[/size][/td][/tr][tr][td][size=100]6.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_segment.png[/icon][/size][/td][td][size=100]Connect points [i]A[/i] and [i]S[/i] using a segment.[/size][/td][/tr][tr][td][size=100]7.[/size][/td][td][icon]https://wiki.geogebra.org/uploads/thumb/e/e2/Menu-trace-on.svg/32px-Menu-trace-on.svg.png[/icon][/td][td][size=100]Turn on the trace of point [i]S[/i]. [br][b]Hint:[/b] Right-click point [i]S[/i] (MacOS: Ctrl-click, tablet: long click) and select [i]Show Trace[/i].[br][/size][/td][/tr][tr][td][size=100]8.[/size][/td][td][br][/td][td][size=100]Right-click (MacOS: Ctrl-click[size=100], tablet: long click[/size]) point [i]A[/i] and choose [i]Animation[/i] from the appearing context menu.[br][b]Hint:[/b] An [i]Animation [/i]button appears in the lower left corner of the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i]. It allows you to either [img]https://wiki.geogebra.org/uploads/thumb/8/82/Nav_pause_circle.svg/16px-Nav_pause_circle.svg.png[/img] pause or [img]https://wiki.geogebra.org/uploads/thumb/e/e8/Nav_play_circle.svg/16px-Nav_play_circle.svg.png[/img] continue an animation.[/size][/td][/tr][/table]