Difference between revisions of "Applications-of-GeoGebra/C3/3D-Geometry/English"

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(Created page with "{|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this tutorial on '''3D Geometry'''. |- | | '''Slide Number 2...")
 
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{|border=1
 
{|border=1
−
| | '''Visual Cue'''
+
||'''Visual Cue'''
−
| | '''Narration'''
+
||'''Narration'''
  
 
|-
 
|-
−
| | '''Slide Number 1'''
+
||'''Slide Number 1'''
  
 
'''Title Slide'''
 
'''Title Slide'''
−
| | Welcome to this tutorial on '''3D Geometry'''.
+
||Welcome to this tutorial on '''3D Geometry'''.
 
|-
 
|-
−
| | '''Slide Number 2'''
+
||'''Slide Number 2'''
  
 
'''Learning Objectives'''
 
'''Learning Objectives'''
−
| | In this '''tutorial''', we will learn how to use '''GeoGebra''' to view:
+
||In this '''tutorial''', we will learn how to use '''GeoGebra''' to view:
  
 
And construct different structures in '''3D space'''
 
And construct different structures in '''3D space'''
Line 20: Line 20:
 
Trigonometric functions in 3D space
 
Trigonometric functions in 3D space
 
|-
 
|-
−
| | '''Slide Number 3'''
+
||'''Slide Number 3'''
  
 
'''System Requirement'''
 
'''System Requirement'''
−
| | Here I am using:
+
||Here I am using:
  
 
'''Ubuntu Linux''' OS version 16.04
 
'''Ubuntu Linux''' OS version 16.04
Line 29: Line 29:
 
'''GeoGebra''' 5.0.481.0-d
 
'''GeoGebra''' 5.0.481.0-d
 
|-
 
|-
−
| | '''Slide Number 4'''
+
||'''Slide Number 4'''
  
 
'''Pre-requisites'''
 
'''Pre-requisites'''
  
 
'''www.spoken-tutorial.org'''
 
'''www.spoken-tutorial.org'''
−
| | To follow this '''tutorial''', you should be familiar with:
+
||To follow this '''tutorial''', you should be familiar with:
  
 
'''GeoGebra''' interface
 
'''GeoGebra''' interface
Line 42: Line 42:
 
For relevant '''tutorials''', please visit our website.
 
For relevant '''tutorials''', please visit our website.
 
|-
 
|-
−
| | '''Slide Number 5'''
+
||'''Slide Number 5'''
  
 
'''Rectangular Co-ordinate System'''
 
'''Rectangular Co-ordinate System'''
  
 
[[Image:]]
 
[[Image:]]
−
| | This image shows the '''rectangular coordinate system'''.
+
||This image shows the '''rectangular coordinate system'''.
  
 
It is made up of mutually perpendicular axes and planes formed by them.
 
It is made up of mutually perpendicular axes and planes formed by them.
Line 63: Line 63:
 
Point '''A''' is in the '''XOYZ''' octant and has the '''coordinates 4 comma 4 comma 2'''.
 
Point '''A''' is in the '''XOYZ''' octant and has the '''coordinates 4 comma 4 comma 2'''.
 
|-
 
|-
−
| | Show the '''GeoGebra''' window.
+
||Show the '''GeoGebra''' window.
−
| | Let us draw a '''3D''' pyramid in '''GeoGebra'''.
+
||Let us draw a '''3D''' pyramid in '''GeoGebra'''.
  
 
I have already opened a new window in '''GeoGebra'''.
 
I have already opened a new window in '''GeoGebra'''.
Line 70: Line 70:
 
This time, we work with '''Algebra, 2D Graphics''' and '''3D Graphics''' views.
 
This time, we work with '''Algebra, 2D Graphics''' and '''3D Graphics''' views.
 
|-
 
|-
−
| | Under '''View''', select '''3D Graphics'''.
+
||Under '''View''', select '''3D Graphics'''.
−
| | Under '''View''', select '''3D Graphics'''.
+
||Under '''View''', select '''3D Graphics'''.
 
|-
 
|-
−
| | Click in '''2D Graphics View''' to draw in '''2D'''.
+
||Click in '''2D Graphics View''' to draw in '''2D'''.
−
| | Click in '''2D Graphics View''' to draw in '''2D'''.
+
||Click in '''2D Graphics View''' to draw in '''2D'''.
 
|-
 
|-
−
| | Drag the boundary to see '''2D Graphics''' properly.
+
||Drag the boundary to see '''2D Graphics''' properly.
−
| | Drag the boundary to see '''2D Graphics''' properly.
+
||Drag the boundary to see '''2D Graphics''' properly.
 
|-
 
|-
−
| | Click in '''2D Graphics'''.
+
||Click in '''2D Graphics'''.
−
| | Click in '''2D Graphics'''.
+
||Click in '''2D Graphics'''.
 
|-
 
|-
−
| | In '''2D Graphics''' view, click on '''Polygon''' tool and click on '''origin (0,0)'''.
+
||In '''2D Graphics''' view, click on '''Polygon''' tool and click on '''origin (0,0)'''.
  
 
Point to '''A'''.
 
Point to '''A'''.
−
| | In '''2D Graphics''' view, click on the '''Polygon''' tool and click on origin 0 comma 0.
+
||In '''2D Graphics''' view, click on the '''Polygon''' tool and click on origin 0 comma 0.
  
 
This creates point '''A''' at the origin.
 
This creates point '''A''' at the origin.
 
|-
 
|-
−
| | Then click on '''(2,0)''' to create point '''B'''.
+
||Then click on '''(2,0)''' to create point '''B'''.
−
| | Then click on 2 comma 0 to create point '''B'''.
+
||Then click on 2 comma 0 to create point '''B'''.
 
|-
 
|-
−
| | Click on '''(2,2)''' for point '''C''', and on '''(0,2)''' to draw point '''D'''.
+
||Click on '''(2,2)''' for point '''C''', and on '''(0,2)''' to draw point '''D'''.
−
| | Click on 2 comma 2 for '''C''' and on 0 comma 2 to draw '''D'''.
+
||Click on 2 comma 2 for '''C''' and on 0 comma 2 to draw '''D'''.
 
|-
 
|-
−
| | Click again on point '''A'''.
+
||Click again on point '''A'''.
−
| | Finally, click again on '''A'''.
+
||Finally, click again on '''A'''.
 
|-
 
|-
−
| | Point to quadrilateral '''q1''' in '''2D''' and '''3D Graphics''' views.
+
||Point to quadrilateral '''q1''' in '''2D''' and '''3D Graphics''' views.
−
| | Note that a quadrilateral '''q1''' is seen in '''2D''' and '''3D Graphics''' views.
+
||Note that a quadrilateral '''q1''' is seen in '''2D''' and '''3D Graphics''' views.
  
  
 
The length of each side is 2 units.
 
The length of each side is 2 units.
 
|-
 
|-
−
| | Click on '''Move''' tool.
+
||Click on '''Move''' tool.
−
| | Click on the '''Move''' tool.
+
||Click on the '''Move''' tool.
 
|-
 
|-
−
| | Click in '''2D Graphics''' and drag the background.
+
||Click in '''2D Graphics''' and drag the background.
−
| | Click in '''2D Graphics''' and drag the background.
+
||Click in '''2D Graphics''' and drag the background.
 
|-
 
|-
−
| | Drag the boundary to see '''3D Graphics''' properly.
+
||Drag the boundary to see '''3D Graphics''' properly.
−
| | Drag the boundary to see '''3D Graphics''' properly.
+
||Drag the boundary to see '''3D Graphics''' properly.
 
|-
 
|-
−
| | Click in '''3D Graphics''' and under '''Pyramid''', on the '''Extrude to Pyramid or Cone''' tool.
+
||Click in '''3D Graphics''' and under '''Pyramid''', on the '''Extrude to Pyramid or Cone''' tool.
  
 
Click on the square in '''3D Graphics''' view.
 
Click on the square in '''3D Graphics''' view.
Line 120: Line 120:
 
In '''3D Graphics''' view, click on the square.
 
In '''3D Graphics''' view, click on the square.
 
|-
 
|-
−
| | An '''Altitude''' text box opens up, type 3 and click '''OK'''.
+
||An '''Altitude''' text box opens up, type 3 and click '''OK'''.
−
| | In the '''Altitude''' text-box that opens, type 3 and click '''OK'''.
+
||In the '''Altitude''' text-box that opens, type 3 and click '''OK'''.
 
|-
 
|-
−
| | Point to pyramid '''e''' in '''3D Graphics''' view.
+
||Point to pyramid '''e''' in '''3D Graphics''' view.
  
 
Point to base.
 
Point to base.
Line 130: Line 130:
  
 
Show altitude.
 
Show altitude.
−
| | A pyramid '''e''' appears in '''3D Graphics''' view.
+
||A pyramid '''e''' appears in '''3D Graphics''' view.
  
 
Its base is the quadrilateral '''q1'''.
 
Its base is the quadrilateral '''q1'''.
Line 138: Line 138:
 
Its altitude or height is 3 units.
 
Its altitude or height is 3 units.
 
|-
 
|-
−
| | '''Slide Number 6'''
+
||'''Slide Number 6'''
  
 
'''Rotation of a Polynomial'''
 
'''Rotation of a Polynomial'''
Line 145: Line 145:
  
 
Part in second '''quadrant''' ('''XY''' plane) about '''x-axis'''
 
Part in second '''quadrant''' ('''XY''' plane) about '''x-axis'''
−
| | '''Rotation of a Polynomial'''
+
||'''Rotation of a Polynomial'''
  
 
Let us rotate '''f of x''' equals minus '''2 x raised to 4''' minus '''x cubed''' plus '''3 x squared'''.
 
Let us rotate '''f of x''' equals minus '''2 x raised to 4''' minus '''x cubed''' plus '''3 x squared'''.
Line 151: Line 151:
 
We will rotate the part that lies in the second '''quadrant''', in '''XY''' plane, about the '''x-axis'''.
 
We will rotate the part that lies in the second '''quadrant''', in '''XY''' plane, about the '''x-axis'''.
 
|-
 
|-
−
| | Show the '''GeoGebra''' window.
+
||Show the '''GeoGebra''' window.
  
  
  
−
| | I have already opened a new window in '''GeoGebra'''.
+
||I have already opened a new window in '''GeoGebra'''.
  
 
We will initially work with '''Algebra''' and '''2D Graphics''' views and open '''3D Graphics''' view later.
 
We will initially work with '''Algebra''' and '''2D Graphics''' views and open '''3D Graphics''' view later.
 
|-
 
|-
−
| | In '''input bar''', type the following line and press '''Enter'''.
+
||In '''input bar''', type the following line and press '''Enter'''.
  
 
'''f(x) = -2 x^4 -x^3+3 x^2'''
 
'''f(x) = -2 x^4 -x^3+3 x^2'''
−
| | In the '''input bar''', type the following line.
+
||In the '''input bar''', type the following line.
  
 
To type the '''caret symbol''', hold '''Shift''' key down and press 6.
 
To type the '''caret symbol''', hold '''Shift''' key down and press 6.
−
 
−
'''f x''' in parentheses equals minus 2 space '''x caret''' 4 minus '''x caret''' 3 plus 3 space '''x caret''' 2
 
  
 
Spaces here denote multiplication.
 
Spaces here denote multiplication.
Line 172: Line 170:
 
Press '''Enter'''.
 
Press '''Enter'''.
 
|-
 
|-
−
| | Under '''Perpendicular Line''', click on '''Parallel line''' and on the '''y-axis'''.
+
||Under '''Perpendicular Line''', click on '''Parallel line''' and on the '''y-axis'''.
−
| | Under '''Perpendicular Line''', click on '''Parallel line''' and on the '''y-axis'''.
+
||Under '''Perpendicular Line''', click on '''Parallel line''' and on the '''y-axis'''.
 
|-
 
|-
−
| | Keeping the '''cursor''' on the '''x-axis'''.
+
||Keeping the '''cursor''' on the '''x-axis'''.
−
| | Keep the '''cursor''' on the '''x-axis'''.
+
||Keep the '''cursor''' on the '''x-axis'''.
 
|-
 
|-
−
| | Drag it along until you reach the intersection of '''f''' and '''x-axis'''.
+
||Drag it along until you reach the intersection of '''f''' and '''x-axis'''.
  
 
Point to the label '''function f, x-axis''' that appears.
 
Point to the label '''function f, x-axis''' that appears.
−
| | Drag it along until you see '''function f, x-axis''' at the intersection of '''f''' and '''x-axis'''.
+
||Drag it along until you see '''function f, x-axis''' at the intersection of '''f''' and '''x-axis'''.
 
|-
 
|-
−
| | Click on this intersection point.
+
||Click on this intersection point.
−
| | Click on this intersection point.
+
||Click on this intersection point.
 
|-
 
|-
−
| | Point to '''A'''.
+
||Point to '''A'''.
−
| | Point '''A''' appears.
+
||Point '''A''' appears.
 
|-
 
|-
−
| | Click on '''Slider''' and in '''Graphics''' view.
+
||Click on '''Slider''' and in '''Graphics''' view.
−
| | Click on '''Slider''' and in '''Graphics''' view.
+
||Click on '''Slider''' and in '''Graphics''' view.
 
|-
 
|-
−
| | A '''Slider''' dialog box opens.
+
||A '''Slider''' dialog box opens.
−
| | A '''Slider''' dialog-box opens.
+
||A '''Slider''' dialog-box opens.
 
|-
 
|-
−
| | Leave '''a''' as the '''Name'''.
+
||Leave '''a''' as the '''Name'''.
−
| | Leave '''a''' as the '''Name'''.
+
||Leave '''a''' as the '''Name'''.
 
|-
 
|-
−
| | Change '''Min''' value to -1.5, '''Max''' value to 0 and '''Increment''' to 0.05.
+
||Change '''Min''' value to -1.5, '''Max''' value to 0 and '''Increment''' to 0.05.
−
| | Change '''Min''' value to '''minus''' 1.5, '''Max''' value to 0 and '''Increment''' to 0.05.
+
|| Change '''Min''' value to '''minus''' 1.5, '''Max''' value to 0 and '''Increment''' to 0.05.
 
|-
 
|-
−
| | Click '''OK'''.
+
||Click '''OK'''.
−
| | Click '''OK'''.
+
||Click '''OK'''.
 
|-
 
|-
−
| | Point to '''slider a'''.
+
||Point to '''slider a'''.
  
 
Point to the part of '''function''' and '''x-axis''' in the second '''quadrant'''.
 
Point to the part of '''function''' and '''x-axis''' in the second '''quadrant'''.
−
| | This creates '''slider a''', which changes the value of '''a''' from -1.5 to 0.
+
||This creates '''slider a''', which changes the value of '''a''' from -1.5 to 0.
  
 
It will focus on the part of the graph in the second '''quadrant'''.
 
It will focus on the part of the graph in the second '''quadrant'''.
 
|-
 
|-
−
| | In the '''input bar''', type '''(a,f(a))'''.
+
||In the '''input bar''', type '''(a,f(a))'''.
  
 
Press '''Enter'''.
 
Press '''Enter'''.
−
| | In the '''input bar''', type the following in parentheses.
+
||In the '''input bar''', type the following in parentheses.
  
 
'''a''' comma '''f a''' in parentheses.
 
'''a''' comma '''f a''' in parentheses.
Line 220: Line 218:
 
Press '''Enter'''.
 
Press '''Enter'''.
 
|-
 
|-
−
| | Point to '''B'''.
+
||Point to '''B'''.
−
| | This creates point '''B''' whose '''x coordinate''' is the value of '''a'''.
+
||This creates point '''B''' whose '''x coordinate''' is the value of '''a'''.
  
 
Its '''y-coordinate''' lies along the curve described by the '''function f''' between '''x''' equals  1.5 and 0.
 
Its '''y-coordinate''' lies along the curve described by the '''function f''' between '''x''' equals  1.5 and 0.
 
|-
 
|-
−
| | Right-click on '''slider a''' and check '''Animation On'''.
+
||Right-click on '''slider a''' >> check '''Animation On'''.
−
| | Right-click on '''slider a''' and check '''Animation On'''.
+
||Right-click on '''slider a''' and check '''Animation On'''.
 
|-
 
|-
−
| | Point to '''B''' and '''slider a'''.
+
||Point to '''B''' and '''slider a'''.
−
| | Point '''B''' travels along '''function f''' as '''a''' changes.
+
||Point '''B''' travels along '''function f''' as '''a''' changes.
 
|-
 
|-
−
| | Right-click on '''slider a''' and uncheck '''Animation On'''.
+
||Right-click on '''slider a''' >> uncheck '''Animation On'''.
−
| | Right-click on '''slider a''' and uncheck '''Animation On'''.
+
||Right-click on '''slider a''' and uncheck '''Animation On'''.
 
|-
 
|-
−
| | In the '''input bar''', type '''(a,0)''' and press '''Enter'''.
+
||In the '''input bar''', type '''(a,0)''' >> press '''Enter'''.
−
| | In the '''input bar''', type '''a''' comma 0 in parentheses and press '''Enter'''.
+
||In the '''input bar''', type '''a''' comma 0 in parentheses and press '''Enter'''.
 
|-
 
|-
−
| | Point to '''C''' and '''slider a'''.
+
||Point to '''C''' and '''slider a'''.
−
| | This creates point '''C'''.
+
||This creates point '''C'''.
 
   
 
   
 
As its '''x co-ordinate a''' changes, '''C''' moves below point '''B''' along the '''x-axis'''.
 
As its '''x co-ordinate a''' changes, '''C''' moves below point '''B''' along the '''x-axis'''.
 
|-
 
|-
−
| | Under '''Line''', click on '''Segment''' and click on '''B''' and '''C''' to join them.
+
||Under '''Line''', click on '''Segment''' >> click on '''B''' and '''C''' to join them.
−
| | Under '''Line''', click on '''Segment''' and click on '''B''' and '''C''' to join them.
+
||Under '''Line''', click on '''Segment''' and click on '''B''' and '''C''' to join them.
 
|-
 
|-
−
| | Click on '''Move Graphics View''' and drag background to the left.
+
||Click on '''Move Graphics View''' >> drag background to the left.
−
| | Click on '''Move Graphics View''' and drag the background to the left.
+
||Click on '''Move Graphics View''' and drag the background to the left.
 
|-
 
|-
−
| | Click on '''View''' and check '''3D Graphics''' to see the '''3D Graphics''' view.
+
||Click on '''View''' >> check '''3D Graphics''' to see the '''3D Graphics''' view.
−
| | Click on '''View''' and check '''3D Graphics''' to see the '''3D Graphics''' view.
+
||Click on '''View''' and check '''3D Graphics''' to see the '''3D Graphics''' view.
 
|-
 
|-
−
| | Point to '''2D Graphics''' and  '''3D Graphics''' views.
+
||Point to '''2D Graphics''' and  '''3D Graphics''' views.
−
| | Note that what is drawn in '''2D Graphics''' appears in the '''XY''' plane, in '''3D Graphics'''.
+
||Note that what is drawn in '''2D Graphics''' appears in the '''XY''' plane, in '''3D Graphics'''.
 
|-
 
|-
−
| | Click in '''3D Graphics''' view and on '''Rotate 3D Graphics View'''.
+
||Click in '''3D Graphics''' view >> on '''Rotate 3D Graphics View'''.
  
 
Rotate the '''3D Graphics''' view to see the curve properly.
 
Rotate the '''3D Graphics''' view to see the curve properly.
−
| | Click in '''3D Graphics''' view and on '''Rotate 3D Graphics View'''.
+
||Click in '''3D Graphics''' view and on '''Rotate 3D Graphics View'''.
  
 
Rotate '''3D Graphics''' to see the curve properly.
 
Rotate '''3D Graphics''' to see the curve properly.
 
|-
 
|-
−
| | Place '''cursor''' on '''y-axis''' (in green).
+
||Place '''cursor''' on '''y-axis''' (in green).
  
 
Click to see an arrow aligned with the '''y-axis'''.
 
Click to see an arrow aligned with the '''y-axis'''.
−
| | Place the '''cursor''' on the '''y-axis''' (in green).
+
||Place the '''cursor''' on the '''y-axis''' (in green).
  
 
Click to see an arrow aligned with the '''y-axis'''.
 
Click to see an arrow aligned with the '''y-axis'''.
 
|-
 
|-
−
| | Then, drag along the '''y axis''' to see the curve properly.
+
||Then, drag along the '''y axis''' to see the curve properly.
−
| | Drag to pull the '''y-axis''' in or outwards to see the curve.
+
||Drag to pull the '''y-axis''' in or outwards to see the curve.
 
|-
 
|-
−
| | Type '''Circle[C,f(a),xAxis]''' in the '''input bar''' and press '''Enter'''.
+
||Type '''Circle[C,f(a),xAxis]''' in the '''input bar''' >> press '''Enter'''.
−
| | In the '''input bar''', type the following line
+
||In the '''input bar''', type the following line.
−
 
+
−
'''Circle''' open square brackets '''capital C '''comma '''f a''' in parentheses comma '''x Axis''' with '''capital A'''.
+
  
−
Close square brackets.
 
 
|-
 
|-
−
| | Point to circle '''c''' with center at point '''C'''.
+
||Point to circle '''c''' with center at point '''C'''.
−
| | This creates circle '''c''' with center at point '''C'''.
+
||This creates circle '''c''' with center at point '''C'''.
  
 
Its radius is equal to '''f of a''' corresponding to the value of '''a''' on '''slider a'''.
 
Its radius is equal to '''f of a''' corresponding to the value of '''a''' on '''slider a'''.
Line 287: Line 282:
 
Press '''Enter'''.
 
Press '''Enter'''.
 
|-
 
|-
−
| | Right-click on circle '''c''' in '''Algebra''' view and check '''Trace On''' option.
+
||Right-click on circle '''c''' in '''Algebra''' view and check '''Trace On''' option.
−
| | In '''Algebra''' view, right-click on circle '''c''' and check '''Trace On''' option.
+
||In '''Algebra''' view, right-click on circle '''c''' and check '''Trace On''' option.
 
|-
 
|-
−
| | Right-click on '''slider a''' and select '''Animation On''' option.
+
||Right-click on '''slider a''' >> select '''Animation On''' option.
−
| | Right-click on '''slider a''' and select '''Animation On''' option.
+
||Right-click on '''slider a''' and select '''Animation On''' option.
 
|-
 
|-
−
| | Point to the solid traced as '''a''' changes.
+
||Point to the solid traced as '''a''' changes.
−
| | Observe the solid traced as '''a''' changes.
+
||Observe the solid traced as '''a''' changes.
 
|-
 
|-
−
| | Point to '''2D''' and '''3D Graphics''' views.
+
||Point to '''2D''' and '''3D Graphics''' views.
−
| | Watch both '''2D''' and '''3D Graphics''' views.
+
||Watch both '''2D''' and '''3D Graphics''' views.
 
|-
 
|-
−
| | Point to Segment '''BC''', '''x-axis''' and '''function f'''.
+
||Point to Segment '''BC''', '''x-axis''' and '''function f'''.
−
| | Segment '''BC''' moves between the '''x-axis''' and '''function f'''.
+
||Segment '''BC''' moves between the '''x-axis''' and '''function f'''.
 
|-
 
|-
−
| | Point to the part of '''f''' in the second '''quadrant'''.
+
||Point to the part of '''f''' in the second '''quadrant'''.
−
| | The part of '''function f''' that is in the second '''quadrant''' in '''2D,''' rotates around the '''x-axis'''.
+
||The part of '''function f''' that is in the second '''quadrant''' in '''2D,''' rotates around the '''x-axis'''.
 
|-
 
|-
−
| | Drag '''3D Graphics''' to see it from another angle.
+
||Drag '''3D Graphics''' to see it from another angle.
−
| | Drag '''3D Graphics''' to see it from another angle.
+
||Drag '''3D Graphics''' to see it from another angle.
 
|-
 
|-
−
| | Show the '''GeoGebra''' window.
+
||Show the '''GeoGebra''' window.
−
| | Finally, let us look at '''trigonometric functions''' in '''3D.'''
+
||Finally, let us look at '''trigonometric functions''' in '''3D.'''
  
 
I have already opened a new window in '''GeoGebra'''.
 
I have already opened a new window in '''GeoGebra'''.
 
|-
 
|-
−
| | Click on '''3D Graphics''' tool under '''View'''.
+
||Click on '''3D Graphics''' tool under '''View'''.
−
| | Under '''View''', click on '''3D Graphics'''.
+
||Under '''View''', click on '''3D Graphics'''.
 
|-
 
|-
−
| | Drag the boundary to see '''2D Graphics''' properly.
+
||Drag the boundary to see '''2D Graphics''' properly.
−
| | Drag the boundary to see '''2D Graphics''' properly.
+
||Drag the boundary to see '''2D Graphics''' properly.
 
|-
 
|-
−
| | Click in '''2D Graphics''', then on the '''Slider''' tool and in '''Graphics''' view.
+
||Click in '''2D Graphics'''>> '''Slider''' tool and in '''Graphics''' view.
−
| | Click in '''2D Graphics''', then on the '''Slider''' tool and in '''Graphics''' view.
+
||Click in '''2D Graphics''', then on the '''Slider''' tool and in '''Graphics''' view.
 
|-
 
|-
−
| | Point to the '''slider''' dialog box and '''Number''' radio button selection.
+
||Point to the '''slider''' dialog box and '''Number''' radio button selection.
  
 
Type '''t''' in the '''Name''' field.
 
Type '''t''' in the '''Name''' field.
−
| | A '''slider''' dialog-box opens.
+
||A '''slider''' dialog-box opens.
  
 
By default, the '''Number''' radio-button is selected.
 
By default, the '''Number''' radio-button is selected.
Line 331: Line 326:
 
In the '''Name''' field, type '''t'''.
 
In the '''Name''' field, type '''t'''.
 
|-
 
|-
−
| | Set '''Min''' to -6, '''Max''' to 16 and '''increment''' of 0.1.
+
||Set '''Min''' to -6, '''Max''' to 16 and '''increment''' of 0.1.
  
 
Click '''OK'''.
 
Click '''OK'''.
−
| | Set '''Min''' to minus 6, '''Max''' to 16 and '''increment''' of 0.1.
+
||Set '''Min''' to minus 6, '''Max''' to 16 and '''increment''' of 0.1.
  
 
Click '''OK'''.
 
Click '''OK'''.
 
|-
 
|-
−
| | Point to '''slider t'''.
+
||Point to '''slider t'''.
−
| | This creates a '''slider t''' which will change '''t''' from minus 6 to 16.   
+
||This creates a '''slider t''' which will change '''t''' from minus 6 to 16.   
 
|-
 
|-
−
| | In the '''input bar''', type '''f(t)=cos(t)''' and press '''Enter'''.
+
||In the '''input bar''', type '''f(t)=cos(t)''' >> press '''Enter'''.
−
| | In the '''input bar''', type '''f t''' in parentheses equals '''cos t''' in parentheses and press '''Enter'''.
+
||In the '''input bar''', type '''f t''' in parentheses equals '''cos t''' in parentheses and press '''Enter'''.
 
|-
 
|-
−
| | Click in '''2D Graphics'''.
+
||Click in '''2D Graphics'''.
−
| | Click in '''2D Graphics'''.
+
||Click in '''2D Graphics'''.
 
|-
 
|-
−
| | Under '''Move Graphics View''', click on '''Zoom Out''' and click in '''2D Graphics'''.
+
||Under '''Move Graphics View''', click on '''Zoom Out''' and click in '''2D Graphics'''.
−
| | Under '''Move Graphics View''', click on '''Zoom Out''' and click in '''2D Graphics'''.
+
||Under '''Move Graphics View''', click on '''Zoom Out''' and click in '''2D Graphics'''.
 
|-
 
|-
−
| | Click on '''Move Graphics View''' and drag the background.
+
||Click on '''Move Graphics View''' >> drag the background.
−
| | Click on '''Move Graphics View''' and drag the background.
+
||Click on '''Move Graphics View''' and drag the background.
 
|-
 
|-
−
| | Point to the '''cosine function''' of '''f(t)''' in '''2D''' and '''3D Graphics''' views.
+
||Point to the '''cosine function''' of '''f(t)''' in '''2D''' and '''3D Graphics''' views.
−
| | You can see the graph of the '''cosine function''' of '''f of t''', in '''2D''' and '''3D Graphics''' views.
+
||You can see the graph of the '''cosine function''' of '''f of t''', in '''2D''' and '''3D Graphics''' views.
 
|-
 
|-
−
| | Similarly, type '''g(t)=sin(t)''' in the '''input bar''' and press '''Enter'''.
+
||Type '''g(t)=sin(t)''' in the '''input bar''' >> press '''Enter'''.
−
| | Similarly, in the '''input bar''', type '''g t''' in parentheses equals '''sin t''' in parentheses.
+
||Similarly, in the '''input bar''', type '''g t''' in parentheses equals '''sin t''' in parentheses.
  
 
Press '''Enter'''.
 
Press '''Enter'''.
 
|-
 
|-
−
| | Point to '''sine function''' graph ('''g(t)''').
+
||Point to '''sine function''' graph ('''g(t)''').
−
| | '''Sine function''' graph of '''g of t''' appears.   
+
||'''Sine function''' graph of '''g of t''' appears.   
 
|-
 
|-
−
| | Now, type '''h(t)=t/4''' in the '''input bar''' and press '''Enter'''.
+
||Type '''h(t)=t/4''' in the '''input bar''' >> press '''Enter'''.
−
| | In the '''input bar''', type '''h t''' in parentheses equals '''t''' divided by 4 and press '''Enter'''.
+
||In the '''input bar''', type '''h t''' in parentheses equals '''t''' divided by 4 and press '''Enter'''.
 
|-
 
|-
−
| | Point to line ('''h(t)''').
+
||Point to line ('''h(t)''').
−
| | Line '''h of t''' is of the form '''y''' equals '''mx''' where slope '''m''' is 1 divided by 4.
+
||Line '''h of t''' is of the form '''y''' equals '''mx''' where slope '''m''' is 1 divided by 4.
 
|-
 
|-
−
| | Click in '''3D Graphics''' view.
+
||Click in '''3D Graphics''' view.
−
| | Click in '''3D Graphics''' view.
+
||Click in '''3D Graphics''' view.
 
|-
 
|-
−
| | Click on '''Point''' tool and click in the gray area in '''3D Graphics''' view.
+
||Click on '''Point''' tool >> click in the gray area in '''3D Graphics''' view.
  
 
Point to point '''A'''.
 
Point to point '''A'''.
−
| | Click on the '''Point''' tool and click in the gray area in '''3D Graphics''' view.
+
||Click on the '''Point''' tool and click in the gray area in '''3D Graphics''' view.
  
 
This creates point '''A'''.
 
This creates point '''A'''.
 
|-
 
|-
−
| | Drag the boundary to see its '''co-ordinates''' properly.
+
||Drag the boundary to see its '''co-ordinates''' properly.
−
| | Drag the boundary to see its '''co-ordinates''' properly.
+
||Drag the boundary to see its '''co-ordinates''' properly.
 
|-
 
|-
−
| | Double click on point '''A''' in '''Algebra''' view.
+
||Double click on point '''A''' in '''Algebra''' view.
  
 
Change the '''co-ordinates''' to '''(f(t),g(t),h(t))'''.
 
Change the '''co-ordinates''' to '''(f(t),g(t),h(t))'''.
  
 
Press '''Enter'''.
 
Press '''Enter'''.
−
| | In '''Algebra''' view, double-click on '''A'''.
+
||In '''Algebra''' view, double-click on '''A'''.
  
−
Change the '''coordinates''' to the following.
+
Change the '''coordinates''' to the following. Press '''Enter'''.
 
|-
 
|-
−
| | Point to '''A'''.
+
||Point to '''A'''.
−
| | The '''x- coordinate''' of '''A''' is '''cos t'''.
+
||The '''x- coordinate''' of '''A''' is '''cos t'''.
  
 
The '''y-coordinate''' is  '''sin t''' and '''t''' divided by '''4''' is its '''z coordinate'''.
 
The '''y-coordinate''' is  '''sin t''' and '''t''' divided by '''4''' is its '''z coordinate'''.
 
|-
 
|-
−
| | Right-click on '''slider t''' and click on '''Object Properties'''.
+
||Right-click on '''slider t''' >> click on '''Object Properties'''.
−
| | Right-click on '''slider t''' and click on '''Object Properties'''.
+
||Right-click on '''slider t''' and click on '''Object Properties'''.
 
|-
 
|-
−
| | A '''Preferences''' dialog-box opens.
+
||A '''Preferences''' dialog-box opens.
  
 
Click on '''Slider''' tab.
 
Click on '''Slider''' tab.
  
 
Under '''Animation''', for '''Repeat''', choose option “'''Increasing'''” from dropdown menu.
 
Under '''Animation''', for '''Repeat''', choose option “'''Increasing'''” from dropdown menu.
−
| | A '''Preferences''' dialog-box opens.
+
|| A '''Preferences''' dialog-box opens.
  
 
Click on '''Slider''' tab.
 
Click on '''Slider''' tab.
Line 411: Line 406:
 
Under '''Animation''', for '''Repeat''', choose option “'''Increasing'''” from the dropdown menu.
 
Under '''Animation''', for '''Repeat''', choose option “'''Increasing'''” from the dropdown menu.
 
|-
 
|-
−
| | Close the '''Preferences''' dialog box.
+
||Close the '''Preferences''' dialog box.
−
| | Close the '''Preferences''' dialog box.
+
||Close the '''Preferences''' dialog box.
 
|-
 
|-
−
| | Right-click on point '''A''' in '''Algebra''' view and select '''Trace On'''.
+
||Right-click on point '''A''' in '''Algebra''' view >> select '''Trace On'''.
−
| | In '''Algebra''' view, right-click on '''A''' and select '''Trace On'''.
+
||In '''Algebra''' view, right-click on '''A''' and select '''Trace On'''.
 
|-
 
|-
−
| | Right-click on '''slider t''' and check '''Animation On'''.
+
||Right-click on '''slider t''' >> check '''Animation On'''.
−
| | Right-click on '''slider t''' and check '''Animation On'''.
+
||Right-click on '''slider t''' and check '''Animation On'''.
 
|-
 
|-
−
| | Point to point '''A''' and the '''helix''' in '''3D Graphics''' view.
+
||Point to point '''A''' and the '''helix''' in '''3D Graphics''' view.
  
 
Point to point '''A’s co-ordinates''' in '''Algebra''' view.
 
Point to point '''A’s co-ordinates''' in '''Algebra''' view.
−
| | Point '''A''' traces a '''helix''' in '''3D''' space with '''coordinates''' mentioned earlier.
+
||Point '''A''' traces a '''helix''' in '''3D''' space with '''coordinates''' mentioned earlier.
 
|-
 
|-
−
| | Click in '''Rotate 3D Graphic View''' and rotate the background.
+
||Click in '''Rotate 3D Graphic View''' >> rotate the background.
  
 
Rotate '''3D Graphics''' view.
 
Rotate '''3D Graphics''' view.
−
| | Click in '''Rotate 3D Graphic View''' and rotate the background.
+
||Click in '''Rotate 3D Graphic View''' and rotate the background.
  
 
Rotate '''3D Graphics''' view so you are looking down the '''z-axis''' at the '''XY''' plane.
 
Rotate '''3D Graphics''' view so you are looking down the '''z-axis''' at the '''XY''' plane.
 
|-
 
|-
−
| | Point to the traces of point '''A (cos(t), sin(t))'''.
+
||Point to the traces of point '''A (cos(t), sin(t))'''.
−
| | Note that the traces of '''A''' are the circumference of a '''unit circle'''.
+
||Note that the traces of '''A''' are the circumference of a '''unit circle'''.
  
 
Point '''A''' moves along the circle as angle '''t''' changes.
 
Point '''A''' moves along the circle as angle '''t''' changes.
Line 439: Line 434:
 
In '''2D''', its '''coordinates''' are '''cos t''' comma '''sin t'''.
 
In '''2D''', its '''coordinates''' are '''cos t''' comma '''sin t'''.
 
|-
 
|-
−
| |
+
||
−
| | Let us summarize.
+
||Let us summarize.
 
|-
 
|-
−
| | '''Slide Number 6'''
+
||'''Slide Number 6'''
  
 
'''Summary'''
 
'''Summary'''
−
| | In this '''tutorial''', we have learnt how to use '''GeoGebra''' to view:
+
||In this '''tutorial''', we have learnt how to use '''GeoGebra''' to view:
  
 
And construct different structures in '''3D''' space
 
And construct different structures in '''3D''' space
Line 453: Line 448:
 
'''Trigonometric functions''' in '''3D''' space
 
'''Trigonometric functions''' in '''3D''' space
 
|-
 
|-
−
| | '''Slide Number 7'''
+
||'''Slide Number 7'''
  
 
'''Assignment'''
 
'''Assignment'''
Line 464: Line 459:
  
 
Show the solid formed due to rotation of peak in first '''quadrant''' in '''XY''' plane.
 
Show the solid formed due to rotation of peak in first '''quadrant''' in '''XY''' plane.
−
| | As an assignment:
+
||As an assignment:
  
 
Construct a prism and a cylinder anywhere in '''3D''' space.
 
Construct a prism and a cylinder anywhere in '''3D''' space.
Line 474: Line 469:
 
Show the solid formed due to rotation of the peak, in the first '''quadrant''', in the '''XY''' plane.
 
Show the solid formed due to rotation of the peak, in the first '''quadrant''', in the '''XY''' plane.
 
|-
 
|-
−
| | '''Slide Number 8'''
+
||'''Slide Number 8'''
  
 
'''Assignment'''
 
'''Assignment'''
Line 485: Line 480:
  
 
How high is the cliff?
 
How high is the cliff?
−
| | As another assignment,
+
|| As another assignment,
  
 
You tried to fly a kite off a cliff. The kite got dumped into the lake below.
 
You tried to fly a kite off a cliff. The kite got dumped into the lake below.
Line 495: Line 490:
 
How high is the cliff?
 
How high is the cliff?
 
|-
 
|-
−
| | '''Slide Number 8'''
+
||'''Slide Number 8'''
  
 
'''About Spoken Tutorial Project'''
 
'''About Spoken Tutorial Project'''
−
| | The video at the following link summarizes the '''Spoken Tutorial''' project.
+
||The video at the following link summarizes the '''Spoken Tutorial''' project.
  
 
Please download and watch it.
 
Please download and watch it.
 
|-
 
|-
−
| | '''Slide Number 9'''
+
||'''Slide Number 9'''
  
 
'''Spoken Tutorial workshops'''
 
'''Spoken Tutorial workshops'''
−
| | The '''Spoken Tutorial '''project''' '''team:
+
||The '''Spoken Tutorial '''project''' '''team:
  
 
<nowiki* conducts workshops using spoken tutorials and</nowiki>
 
<nowiki* conducts workshops using spoken tutorials and</nowiki>
Line 513: Line 508:
 
For more details, please write to us.
 
For more details, please write to us.
 
|-
 
|-
−
| | '''Slide Number 10'''
+
||'''Slide Number 10'''
  
 
'''Forum for specific questions:'''
 
'''Forum for specific questions:'''
Line 526: Line 521:
  
 
Someone from our team will answer them
 
Someone from our team will answer them
−
| | Please post your timed queries on this forum.
+
||Please post your timed queries on this forum.
 
|-
 
|-
−
| | '''Slide Number 11'''
+
||'''Slide Number 11'''
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''
−
| | '''Spoken Tutorial''' project is funded by NMEICT, MHRD, Government of India.
+
||'''Spoken Tutorial''' project is funded by NMEICT, MHRD, Government of India.
  
 
More information on this mission is available at this link.
 
More information on this mission is available at this link.
 
|-
 
|-
−
| |
+
||
−
| | This is '''Vidhya Iyer''' from '''IIT Bombay,''' signing off.
+
||This is '''Vidhya Iyer''' from '''IIT Bombay,''' signing off.
  
 
Thank you for joining.
 
Thank you for joining.
 
|-
 
|-
 
|}
 
|}

Revision as of 12:22, 24 October 2018

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this tutorial on 3D Geometry.
Slide Number 2

Learning Objectives

In this tutorial, we will learn how to use GeoGebra to view:

And construct different structures in 3D space

Solids of rotation of polynomial functions

Trigonometric functions in 3D space

Slide Number 3

System Requirement

Here I am using:

Ubuntu Linux OS version 16.04

GeoGebra 5.0.481.0-d

Slide Number 4

Pre-requisites

www.spoken-tutorial.org

To follow this tutorial, you should be familiar with:

GeoGebra interface

Geometry

For relevant tutorials, please visit our website.

Slide Number 5

Rectangular Co-ordinate System

[[Image:]]

This image shows the rectangular coordinate system.

It is made up of mutually perpendicular axes and planes formed by them.

The axes are x (in red), y (in green) and z (in blue).

All points in 3D space are denoted by their x y z coordinates.

The point of intersection of the three axes is the origin O 0 comma 0 comma 0.

The gray rectangle in the image depicts the XY plane.

The planes divide space into 8 octants.

Point A is in the XOYZ octant and has the coordinates 4 comma 4 comma 2.

Show the GeoGebra window. Let us draw a 3D pyramid in GeoGebra.

I have already opened a new window in GeoGebra.

This time, we work with Algebra, 2D Graphics and 3D Graphics views.

Under View, select 3D Graphics. Under View, select 3D Graphics.
Click in 2D Graphics View to draw in 2D. Click in 2D Graphics View to draw in 2D.
Drag the boundary to see 2D Graphics properly. Drag the boundary to see 2D Graphics properly.
Click in 2D Graphics. Click in 2D Graphics.
In 2D Graphics view, click on Polygon tool and click on origin (0,0).

Point to A.

In 2D Graphics view, click on the Polygon tool and click on origin 0 comma 0.

This creates point A at the origin.

Then click on (2,0) to create point B. Then click on 2 comma 0 to create point B.
Click on (2,2) for point C, and on (0,2) to draw point D. Click on 2 comma 2 for C and on 0 comma 2 to draw D.
Click again on point A. Finally, click again on A.
Point to quadrilateral q1 in 2D and 3D Graphics views. Note that a quadrilateral q1 is seen in 2D and 3D Graphics views.


The length of each side is 2 units.

Click on Move tool. Click on the Move tool.
Click in 2D Graphics and drag the background. Click in 2D Graphics and drag the background.
Drag the boundary to see 3D Graphics properly. Drag the boundary to see 3D Graphics properly.
Click in 3D Graphics and under Pyramid, on the Extrude to Pyramid or Cone tool.

Click on the square in 3D Graphics view.

Click in 3D Graphics and under Pyramid, on the Extrude to Pyramid or Cone tool.

In 3D Graphics view, click on the square.

An Altitude text box opens up, type 3 and click OK. In the Altitude text-box that opens, type 3 and click OK.
Point to pyramid e in 3D Graphics view.

Point to base.

Point to E (1,1,3).

Show altitude.

A pyramid e appears in 3D Graphics view.

Its base is the quadrilateral q1.

Its apex is E 1 comma 1 comma 3.

Its altitude or height is 3 units.

Slide Number 6

Rotation of a Polynomial

Let us rotate f(x)= ¬2x4-x3+3x2

Part in second quadrant (XY plane) about x-axis

Rotation of a Polynomial

Let us rotate f of x equals minus 2 x raised to 4 minus x cubed plus 3 x squared.

We will rotate the part that lies in the second quadrant, in XY plane, about the x-axis.

Show the GeoGebra window.


I have already opened a new window in GeoGebra.

We will initially work with Algebra and 2D Graphics views and open 3D Graphics view later.

In input bar, type the following line and press Enter.

f(x) = -2 x^4 -x^3+3 x^2

In the input bar, type the following line.

To type the caret symbol, hold Shift key down and press 6.

Spaces here denote multiplication.

Press Enter.

Under Perpendicular Line, click on Parallel line and on the y-axis. Under Perpendicular Line, click on Parallel line and on the y-axis.
Keeping the cursor on the x-axis. Keep the cursor on the x-axis.
Drag it along until you reach the intersection of f and x-axis.

Point to the label function f, x-axis that appears.

Drag it along until you see function f, x-axis at the intersection of f and x-axis.
Click on this intersection point. Click on this intersection point.
Point to A. Point A appears.
Click on Slider and in Graphics view. Click on Slider and in Graphics view.
A Slider dialog box opens. A Slider dialog-box opens.
Leave a as the Name. Leave a as the Name.
Change Min value to -1.5, Max value to 0 and Increment to 0.05. Change Min value to minus 1.5, Max value to 0 and Increment to 0.05.
Click OK. Click OK.
Point to slider a.

Point to the part of function and x-axis in the second quadrant.

This creates slider a, which changes the value of a from -1.5 to 0.

It will focus on the part of the graph in the second quadrant.

In the input bar, type (a,f(a)).

Press Enter.

In the input bar, type the following in parentheses.

a comma f a in parentheses.

Press Enter.

Point to B. This creates point B whose x coordinate is the value of a.

Its y-coordinate lies along the curve described by the function f between x equals 1.5 and 0.

Right-click on slider a >> check Animation On. Right-click on slider a and check Animation On.
Point to B and slider a. Point B travels along function f as a changes.
Right-click on slider a >> uncheck Animation On. Right-click on slider a and uncheck Animation On.
In the input bar, type (a,0) >> press Enter. In the input bar, type a comma 0 in parentheses and press Enter.
Point to C and slider a. This creates point C.

As its x co-ordinate a changes, C moves below point B along the x-axis.

Under Line, click on Segment >> click on B and C to join them. Under Line, click on Segment and click on B and C to join them.
Click on Move Graphics View >> drag background to the left. Click on Move Graphics View and drag the background to the left.
Click on View >> check 3D Graphics to see the 3D Graphics view. Click on View and check 3D Graphics to see the 3D Graphics view.
Point to 2D Graphics and 3D Graphics views. Note that what is drawn in 2D Graphics appears in the XY plane, in 3D Graphics.
Click in 3D Graphics view >> on Rotate 3D Graphics View.

Rotate the 3D Graphics view to see the curve properly.

Click in 3D Graphics view and on Rotate 3D Graphics View.

Rotate 3D Graphics to see the curve properly.

Place cursor on y-axis (in green).

Click to see an arrow aligned with the y-axis.

Place the cursor on the y-axis (in green).

Click to see an arrow aligned with the y-axis.

Then, drag along the y axis to see the curve properly. Drag to pull the y-axis in or outwards to see the curve.
Type Circle[C,f(a),xAxis] in the input bar >> press Enter. In the input bar, type the following line.
Point to circle c with center at point C. This creates circle c with center at point C.

Its radius is equal to f of a corresponding to the value of a on slider a.

Its rotation is around the x-axis.

Press Enter.

Right-click on circle c in Algebra view and check Trace On option. In Algebra view, right-click on circle c and check Trace On option.
Right-click on slider a >> select Animation On option. Right-click on slider a and select Animation On option.
Point to the solid traced as a changes. Observe the solid traced as a changes.
Point to 2D and 3D Graphics views. Watch both 2D and 3D Graphics views.
Point to Segment BC, x-axis and function f. Segment BC moves between the x-axis and function f.
Point to the part of f in the second quadrant. The part of function f that is in the second quadrant in 2D, rotates around the x-axis.
Drag 3D Graphics to see it from another angle. Drag 3D Graphics to see it from another angle.
Show the GeoGebra window. Finally, let us look at trigonometric functions in 3D.

I have already opened a new window in GeoGebra.

Click on 3D Graphics tool under View. Under View, click on 3D Graphics.
Drag the boundary to see 2D Graphics properly. Drag the boundary to see 2D Graphics properly.
Click in 2D Graphics>> Slider tool and in Graphics view. Click in 2D Graphics, then on the Slider tool and in Graphics view.
Point to the slider dialog box and Number radio button selection.

Type t in the Name field.

A slider dialog-box opens.

By default, the Number radio-button is selected.

In the Name field, type t.

Set Min to -6, Max to 16 and increment of 0.1.

Click OK.

Set Min to minus 6, Max to 16 and increment of 0.1.

Click OK.

Point to slider t. This creates a slider t which will change t from minus 6 to 16.
In the input bar, type f(t)=cos(t) >> press Enter. In the input bar, type f t in parentheses equals cos t in parentheses and press Enter.
Click in 2D Graphics. Click in 2D Graphics.
Under Move Graphics View, click on Zoom Out and click in 2D Graphics. Under Move Graphics View, click on Zoom Out and click in 2D Graphics.
Click on Move Graphics View >> drag the background. Click on Move Graphics View and drag the background.
Point to the cosine function of f(t) in 2D and 3D Graphics views. You can see the graph of the cosine function of f of t, in 2D and 3D Graphics views.
Type g(t)=sin(t) in the input bar >> press Enter. Similarly, in the input bar, type g t in parentheses equals sin t in parentheses.

Press Enter.

Point to sine function graph (g(t)). Sine function graph of g of t appears.
Type h(t)=t/4 in the input bar >> press Enter. In the input bar, type h t in parentheses equals t divided by 4 and press Enter.
Point to line (h(t)). Line h of t is of the form y equals mx where slope m is 1 divided by 4.
Click in 3D Graphics view. Click in 3D Graphics view.
Click on Point tool >> click in the gray area in 3D Graphics view.

Point to point A.

Click on the Point tool and click in the gray area in 3D Graphics view.

This creates point A.

Drag the boundary to see its co-ordinates properly. Drag the boundary to see its co-ordinates properly.
Double click on point A in Algebra view.

Change the co-ordinates to (f(t),g(t),h(t)).

Press Enter.

In Algebra view, double-click on A.

Change the coordinates to the following. Press Enter.

Point to A. The x- coordinate of A is cos t.

The y-coordinate is sin t and t divided by 4 is its z coordinate.

Right-click on slider t >> click on Object Properties. Right-click on slider t and click on Object Properties.
A Preferences dialog-box opens.

Click on Slider tab.

Under Animation, for Repeat, choose option “Increasing” from dropdown menu.

A Preferences dialog-box opens.

Click on Slider tab.

Under Animation, for Repeat, choose option “Increasing” from the dropdown menu.

Close the Preferences dialog box. Close the Preferences dialog box.
Right-click on point A in Algebra view >> select Trace On. In Algebra view, right-click on A and select Trace On.
Right-click on slider t >> check Animation On. Right-click on slider t and check Animation On.
Point to point A and the helix in 3D Graphics view.

Point to point A’s co-ordinates in Algebra view.

Point A traces a helix in 3D space with coordinates mentioned earlier.
Click in Rotate 3D Graphic View >> rotate the background.

Rotate 3D Graphics view.

Click in Rotate 3D Graphic View and rotate the background.

Rotate 3D Graphics view so you are looking down the z-axis at the XY plane.

Point to the traces of point A (cos(t), sin(t)). Note that the traces of A are the circumference of a unit circle.

Point A moves along the circle as angle t changes.

In 2D, its coordinates are cos t comma sin t.

Let us summarize.
Slide Number 6

Summary

In this tutorial, we have learnt how to use GeoGebra to view:

And construct different structures in 3D space

Solids of rotation of polynomial functions

Trigonometric functions in 3D space

Slide Number 7

Assignment

Construct a prism and a cylinder.

Draw lines to pierce the structures and find their intersection points.

Graph the polynomial, f(x)=x5-7x4+9x3+23x2-50x+24.

Show the solid formed due to rotation of peak in first quadrant in XY plane.

As an assignment:

Construct a prism and a cylinder anywhere in 3D space.

Draw lines to pierce the structures and find their intersection points.

Graph the given polynomial.

Show the solid formed due to rotation of the peak, in the first quadrant, in the XY plane.

Slide Number 8

Assignment

You tried to fly a kite off a cliff. The kite got dumped into the lake below

You gave out 325 feet of string

The angle of declination from where you stand at the cliff’s edge to the kite is 15 degrees

How high is the cliff?

As another assignment,

You tried to fly a kite off a cliff. The kite got dumped into the lake below.

You gave out 325 feet of string.

The angle of declination from where you stand at the cliff’s edge to the kite is 15 degrees.

How high is the cliff?

Slide Number 8

About Spoken Tutorial Project

The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

Slide Number 9

Spoken Tutorial workshops

The Spoken Tutorial project team:

<nowiki* conducts workshops using spoken tutorials and</nowiki>

* gives certificates on passing online tests.

For more details, please write to us.

Slide Number 10

Forum for specific questions:

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question

Explain your question briefly

Someone from our team will answer them

Please post your timed queries on this forum.
Slide Number 11

Acknowledgement

Spoken Tutorial project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

This is Vidhya Iyer from IIT Bombay, signing off.

Thank you for joining.

Contributors and Content Editors

Madhurig, Snehalathak, Vidhya

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