Create an applet to observe the motion of a point on a sphere when changing its spherical coordinates.

[table][tr][td]1.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_sphere2.png[/icon][/td][td]Activate the [size=100][i][i]Sphere with Center through Point[/i][/i] tool from the [i]3D Graphics View Toolbar[/i].[/size] Click on the points [i](0, 0, 0)[/i] and [i](0, 0, 1)[/i] to create a sphere.[/td][/tr][tr][td]2.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_slider.png[/icon][/td][td]Select the [i]Slider[/i] tool from the [i]Graphics View Toolbar[/i] and create a slider for angle [math]\alpha[/math]. [size=100]Use the default settings for sliders and select [i]Apply[/i].[/size][br][/td][/tr][tr][td]3.[/td][td][icon]/images/ggb/toolbar/mode_slider.png[/icon][/td][td]Click in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img][size=100][/size] [i]Graphics View[/i] again to create a second slider [math]\beta[/math] with default settings.[br][/td][/tr][tr][td]4.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][/td][td]Enter [code]r = 1 [/code]into the[i] Input Bar[/i].[br][/td][/tr][tr][td]5.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][/td][td]Enter the conversion of spherical coordinates for point [i]P[/i] into the[i] Input Bar[/i]:[br][math]X=r\cdot cos\left(\alpha\right)\cdot sin\left(\beta\right)[/math][br][math]Y=r\cdot sin\left(\alpha\right)\cdot cos\left(\beta\right)[/math][br][math]Z=r\cdot cos\left(\beta\right)[/math][/td][/tr][tr][td]6.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][/td][td]Enter the point[code] [/code][code]P = (X, Y, Z) [/code]into the [i]Input Bar[/i].[br][/td][/tr][tr][td]7.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][/td][td]Enter[code] [/code][code]Segment((0, 0, 0), P)[br][/code]into the [i]Input Bar[/i] to create a segment between the point of origin to the point [i]P[/i].[br][/td][/tr][tr][td]8.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/c/c5/Stylingbar_icon_graphics3D.svg/32px-Stylingbar_icon_graphics3D.svg.png[/img][/td][td][size=100]Enhance your construction using the [i]Style Bar[/i].[/size][br][/td][/tr][tr][td]9.[/td][td][icon]/images/ggb/toolbar/mode_move.png[/icon][/td][td]Activate the [i]Move[/i] tool and explore the motion of the point [i]P[/i] by dragging the sliders.[/td][/tr][/table]

Just like in the 2D drawing window, you can define the individual coordinate numbers of a point P as a separate number in the 3D drawing window.[br][br][list][*]The cartesian coordinates of a point P are determined as [b](x(P), y(P), z(P))[/b]. With [b]x(P)[/b], [b]y(P)[/b], [b]z(P)[/b] you create separate numbers for the coordinates of point P.[br][/*][/list][list][*]spherical coordinates: P is determined as (abs(P), arg(P), alt(P)). [/*][/list][b]   abs(P)[/b] determines the distance from the origin to the point P [br][b]   arg(P)[/b] determines in the xOy plane the angle between the x-axis, the origin and the point (x(P), y(P), 0).[br][b]   alt(P)[/b] determines the vertical angle between the point (x(P), y(P), 0), the origin and the point P.[br]